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HSC Physics Option Topic

From QUANTA to QUARKS
What is this topic about?
To keep it as simple as possible, (K.I.S.S.) this topic involves the study of:
1. RUTHERFORD & BOHR MODELS OF THE ATOM
2. DE BROGLIE & MATTER WAVES
3. INTO THE NUCLEUS
4. APPLICATIONS OF NUCLEAR PHYSICS
...all in the context of the history, nature and practice of Physics.

1. RUTHERFORD & BOHR MODELS OF THE ATOM
What Has Gone Before...

The Rutherford Model of the Atom

The entire Science of Chemistry and much of
Physics is built on the foundation of Atomic
Theory... the concept that all matter is composed of atoms.

In 1911, Ernest Rutherford carried out an experiment which indicated that the positively charged part
of an atom must be concentrated into a tiny “nucleus”, with the electrons orbiting around it.

Initially conceived as tiny, unbreakable particles of matter, by the beginning of the 20th century it became apparent that the atom was composed of smaller parts.
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Rutherford’s
ATOM

Atom mostly empty space

In his famous experiment with cathode rays, J.J.Thomson had discovered the (negatively charged) electrons in all atoms.

Nucleus of positively charged matter, possibly made up of of particles

This meant that there also had to be a positive part of each atom.

Rutherford’s model proposed that:
• At the centre is a tiny, dense nucleus with a positive electrical charge.
• The negatively charged electrons orbit around the nucleus.
• The distance from nucleus to the electron orbits is very large compared to the size of the particles, so the atom is mostly empty space.

In 1900, Max Plank had proposed the Quantum
Theory to explain the details of the “Black Body
Radiation Curves”.
In 1905, Einstein then explained the strange phenomenon of the Photoelectric Effect by using Plank’s quantum idea. He proposed that light is not just a wave, nor a stream of particles, but made up of “wave packets”.
Light is NOT a stream of particles...

Since negative charge was carried by particles
(the electrons) Rutherford thought it likely that the nucleus was made of positive particles.
These were soon called “protons” and their existence was confirmed a few years later.

Light is NOT a wave...

Light is a stream of “wave packets”... “PHOTONS”

The electrons were too light to account for much of the mass of an atom, so he thought the protons must be relatively heavy.

Each photon is both a particle AND a wave!

Even at this early stage there was speculation that there might be another massive particle in the nucleus as well, but its discovery had to wait
20 years.

Einstein also proposed his “Theory of
Relativity” in 1905. Classical Physics was being turned upside-down by this sequence of new, fundamental discoveries.
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Electrons in orbit around central nucleus 1

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Problems with Rutherford’s Atom

Practical Work

Even as he proposed his atomic model, Rutherford knew there was a problem with it.

Emission Spectrum of Hydrogen
You will have observed the emission spectrum for hydrogen by using a spectrometer to view the light from a discharge tube filled with lowpressure hydrogen gas.

The existing theory of Electromagnetic Radiation
(EMR) contained the concept that if an electrically charged particle was accelerating, then it must emit
EMR, in the form of light waves.

High Voltage

from induction coil

Tube filled with Hydrogen gas

Since Rutherford’s electrons were imagined to be in circular orbits around the nucleus, and since circular motion involves constant (centripital) acceleration, then it follows that each electron should be constantly emitting light. Trouble is... they obviously don’t! Existing accepted theory required that an orbiting electron should emit light energy continuously.
Obviously they don’t, or all matter would constantly glow with light.
However, atoms DO emit light if stimulated with energy, such as in a high-voltage discharge tube. v light emission from electrons Optical viewing system

“Telescope” can be rotated to view the different “lines” of the emission spectrum

Tube glows with emitted light The Balmer Series &
Rhydberg Equation
The lines in the emission spectrum of hydrogen had been discovered some 20 years before
Rutherford’s work, and were known as the
“Balmer Series”.

white light is a mixture of wavelengths different wavelengths spread out to form a spectrum

(use your imagination... we can’t print colours)

Each line was given a name (Hα, Hβ, Hχ & Hδ) and the precise wavelength of each had been measured. Other similar series of lines were known to exist in the invisible infra-red and ultra violet parts of the EMR spectrum.

Red
Orange
Yellow
Green
Blue

No-one could explain them, but mathematicians
Balmer and (later) Rhydberg had worked out that the exact wavelengths of the hydrogen spectrum lines could be calculated from an empirical equation: Violet

If the light emitted by atoms of a particular element is put through a prism, the spectrum shows very narrow bright lines on a dark background because only certain wavelengths are given out. The pattern of lines is characteristic for each element.
Element
B

Light is only emitted at certain precise wavelengths Prism

Each line is one single wavelength of light.

You should be familiar with the idea of a
“spectrum” of light. For example, if “white” light is passed through a prism, the different wavelengths are separated, and the familiar rainbow colours appear.

Each line is light of one exact wavelength.

Spectroscope

You will have seen that the light from a hydrogen discharge tube is composed of 4 visible bright lines of light.

Emission Spectra

Element
A

Slit & lens

The Rhydberg Equation
2

λ = wavelength of the spectral line (in metres)
RH = the “Rhydberg constant” = 1.097 x 107 nf = an integer number. For the Balmer series nf = 2 ni = an integer number. To calculate the wavelengths of the 4 lines of the Balmer series, ni takes the values 3, 4, 5 or 6.

Each element has its own unique set of spectral lines HSC Physics Option Topic “From Quanta to Quarks”
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1 = RH( 1/nf - 1/ni ) λ Element
C

The fact that the Rhydberg equation worked was strong evidence that there was an underlying “law” controlling the hydrogen spectral lines. The fact that a series of integer numbers were involved was a clue that connected the whole thing to Plank’s Quantum Theory...

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Plank’s Quantum Theory

Neils Bohr Puts It All Together

A quick revision of what you learned previously...

Bohr used Plank’s Quantum Theory to modify the
Rutherford model of the atom in such a way that:

In 1900, Max Plank proposed a radical new theory to explain the black body radiation. He found that the only way to explain the exact details coming from the experiments, was that the energy was quantised: emitted or absorbed in “little packets” called “quanta” (singular “quantum”).

• the problem of radiation that should be emitted constantly from accelerating electrons was overcome. • the underlying reasons for emission spectra were explained. • the empirical nature of the Rhydberg Equation was given theoretical backing and mathematical validity.
• the reasons for the “valency” of different atoms, and how and why they combine in fixed ratios became clearer.

The existing theories of “classical” Physics assumed that the amount of energy carried
(say) by a light wave could have any value, on a continuous scale. Plank’s theory was that the energy could only take certain values, based on
“units” or quanta of energy.

Not bad for an afternoon’s work!
(The last point above is fundamental to Chemistry and understanding chemical bonding and formulas. It will not be pursued any further in this topic)

Plank proposed that the amount of energy carried by a “quantum” of light is related to the frequency of the light, and can be calculated as follows:

Bohr’s Postulates
• Electrons revolve only in certain “allowed” orbits.
Bohr theorised that there are a series of orbits, at fixed distances from the nucleus, in which an electron will not constantly emit radiation as demanded by classical theory.
(Why was explained later by de Broglie)

E = h.f
E = energy of a quantum, in joules ( J) h = “Plank’s constant”, value 6.63x10-34

f = frequency of the wave, in hertz (Hz)

“Allowed” orbit positions. Electrons cannot orbit anywhere else.

You are reminded also, of the wave equation:

V = λ.f (or, for light) c = λ.f
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Electrons can “jump” from one orbit to another, but must absorb energy to jump higher, or emit energy to drop lower.

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c = velocity of light (in vacuum) = 3.00x10 ms .

λ = wavelength, in metres (m). f = frequency, in hertz (Hz)

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3

Example Calculation
a) Use the Rhydberg Equation to find the wavelength of the Hδ line of the hydrogen spectrum, given that nf= 2 and ni = 6.
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• Electrons gain or lose energy to “jump” between orbits. To jump up to a higher orbit, an electron must gain a certain quantity of energy. If it drops back to lower orbit, it must emit that exact same amount of energy. 2

1 = RH( 1/nf - 1/ni )

λ

= 1.097x107( 1/22 - 1/62 )

1/λ = 2.438 x 106
∴ λ = 4.10x10-7 m

Quantum numbers of the orbits.
These quantities of energy are “quantised”, so each orbit is really a “quantum energy level” within the atom. (410 nm nanometres)

b) Use the “Wave Equation” to find the frequency. c = λ.f
3.00x108 = 4.10 x10-7x f
∴ f = 3.00x108/4.10x10-7
= 7.32x1014Hz.

The amount of energy absorbed or emitted during a
“jump” is defined by Plank’s Equation E = hf, and the corresponding wavelengths of light are defined by the Rhydberg Equation. The integer numbers nf and ni turn out to be the “quantum numbers” of the orbits, counting outwards from the nucleus.

c) Use Plank’s Equation to calculate the energy carried by one photon of light in the Hδ spectral line.
E = h.f
= 6.63x10-34 x 7.32x1014
= 4.85x10-19 J.

• Electrons in “allowed orbits” have quantised amounts of angular momentum too.
Bohr figured out that the amount of angular momentum possessed by an electron must always be a multiple of h/2π. The significance of this will be dealt with in a later section. HSC Physics Option Topic “From Quanta to Quarks”
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Bohr & the Balmer Series

Limitations of the
Rutherford-Bohr Model

Let’s see how Bohr’s ideas work with regard to the
Balmer Series of hydrogen emission lines.

Despite the way that Bohr’s Postulates seem to solve the problem with Rutherford’s brilliant new concept of the atom, there were still unexplained difficulties.

Bohr suggested that the Hα emission line was due to an electron dropping from the 3rd orbit down to the
2nd orbit. It must lose a precise quantum of energy, so it emits a photon of light at a precise frequency given by E = hf.

Bohr Model worked only for Hydrogen
Hydrogen is the simplest atom, with only one electron and one proton.

In the Rhydberg Equation, ni = 3 and nf = 2. The calculated wavelength (λ) agrees perfectly with the observed spectral line. Plank’s Quantum Equation calculates the energy of that photon of light.

Attempts to apply the model to larger atoms failed, because multiple, orbiting electrons interact with each other as well as the nucleus, and the situation becomes too complex to describe in a simple mathematical way.

Bohr argued that this amount of energy must represent the difference in energy level from orbit 2 to orbit 3.

Different Intensities of Spectral Lines

The other lines of the Balmer Series represent electrons dropping from higher orbits into the 2nd orbit: Hα line. ni = 3 )
Increasing energy nf = 2 difference gives
Hβ line. ni = 4 ) in each case higher frequency
Hχ line. ni = 5 )
(and shorter wavelength) of spectral light
Hδ line. ni = 6 )
It all worked! Bohr’s idea gave a theoretical explanation for the Rhydberg Equation, which had been empirically derived to explain the observed spectral lines.
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light photon emitted

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The different spectral lines showed different intensities or brightness. This means that some orbital “jumps” by electrons always occur more often than others. Bohr’s model had no explanation as to why.

“Hyperfine” Spectral Lines
When the spectral lines were examined more closely, each one was found to be made up of a number of very fine lines close together. iew dv ifie agn
M

Hδ line. ni = 6
Hχ line. ni = 5

4

Hβ line. ni = 4

3

Spectral line is made up of a number of separate, finer lines

Hα line. ni = 3

2
1

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Nucleus

Quantum energy levels or “allowed orbits” around the hydrogen atom

Spectral lines are of different brightness

The Zeeman Effect
When a discharge tube is operated within a magnetic field, each spectral line is split up into several separate lines.

The Hydrogen Spectrum &
Development of Bohr’s Model
Without a knowledge of the emission spectrum of hydrogen, it seems very unlikely that Bohr could have come up with his idea.

This, and the presence of the “hyperfine lines”, suggested that the energy levels or orbits were divided into a number of “sub-orbits” of slightly different energy. Bohr’s model had no explanation for this. The fact that the spectrum shows distinct lines, and that integer numbers are involved in the Rhydberg
Equation, all pointed to some kind of discrete, quantised atomic arrangement, rather than the moreor-less random orbits of Rutherford. Without knowledge of the hydrogen spectrum, (and Plank’s
Quantum Theory) Bohr could not have made the
(literally) quantum leap to his idea.

Like all scientific models, the Rutherford-Bohr atom is a human attempt to explain the observed facts of nature. In its day, this model was the best explanation available, but it was recognised that certain facts remained unexplained.

Like all great scientists, Bohr built on the knowledge discovered by others. His genius was to put it all together in a new synthesis, that helped establish
Rutherford’s new structure of the atom.

This doesn’t make the model wrong... simply incomplete. It was a “work-in-progress”, to be added to and refined by later scientists. This is the way
Science works.

However, there were still some problems...

If further evidence had proven it totally wrong (as can happen) you would not be studying it!

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Summary Worksheet for Section 1 is at the end of the next section
Worksheet 1

Test Questions

section 1

Student Name...............................

1.
Sketch a labelled diagram to show the main features of Rutherford’s atomic model.

5.
The Hχ spectral line for hydrogen is due to an electron dropping from the 5th to the 2nd orbit.
Compared to the Hβ line (in Q3):
a) would a photon of the Hχ line carry more, less, or the same amount of energy? Explain.

2.
Outline the major problem with Rutherford’s atomic model, based on the accepted theory of that time.

b) would the Hχ line have a higher, lower, or the same frequency? Explain.

c) would the Hχ line have a longer, shorter, or the same wavelength? Explain.
3.
a) What is the “Balmer Series”?
6.
a) List, in brief form, 3 of “Bohr’s Postulates”.

b) Calculate the wavelength of the Hβ spectral line for hydrogen, given that ni = 4 and nf = 2.

b) List, in brief form, 4 limitations of the Bohr model. c) Use the wave equation, and Plank’s equation to find the amount of energy carried by one photon of the Hβ line.

d) According to Bohr, what does this amount of energy represent within a hydrogen atom?

7.
It is known that other spectral lines for hydrogen are present in the infra-red and ultra-violet parts of the spectrum. One line, for example, is due to electrons dropping from the 8th to the 1st orbit.
Calculate the wavelength of this spectral line and state if it is infra-red or ultra violet.

4.
Analyse the significance of the hydrogen spectrum in the development of Bohr’s atomic model. HSC Physics Option Topic “From Quanta to Quarks”
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2. DE BROGLIE & MATTER WAVES
Impact of de Broglie’s Hypothesis

de Broglie’s Quantum Proposal

De Broglie’s proposals had almost no impact on the scientific community at first. His mathematics were checked and found to be totally correct. His hypothesis was totally consistent with the Quantum Theory, and with the Bohr model.

Remember that in 1905 Einstein had explained the Photoelectric Effect by suggesting that light has both wave and particle properties. (For this he was awarded the Nobel Prize)
Light is a stream of “wave packets”... “PHOTONS”

The physicists of the day, including Plank,
Einstein, Rutherford and Bohr were all very interested by his work, but it was just a neat mathematical exercise, without any evidence based in experiment or observation.

Each photon is both a particle AND a wave!

Einstein had used Plank’s Quantum Theory to explain a phenomenon that “classical” Physics was unable to explain.

Usually, scientists observe a phenomenon and then try to explain it by theory. de Broglie was putting theory first, without any facts to explain!

In 1924, a young graduate student Louis de
Broglie turned this concept around...

If light waves can have particle-like properties, why can’t particles have wave-like properties?

Eventually, (as happens in Science) an experiment was done to test the hypothesis.
Before learning about that, you need to understand an important wave phenomenon...

Using Quantum Theory and Bohr’s atomic model, de Broglie developed a mathematical model for an electron in orbit around the nucleus acting as a particle with wave properties. Diffraction
Waves can undergo various “wave phenomena” such as reflection, refraction and interference.
In fact, it is these things which can identify waves. For example, it was interference which allowed Hertz to prove the existence of invisible radio waves back in the 1880’s.
De Broglie began from Bohr’s equations which showed that (as a particle) the angular momentum of the electron would be a multiple of h/2π.

Diffraction is something that only waves do.
Barrier

From this he was able to show that (when showing its wave properties) the electron would have a wavelength related to its mass and velocity: with gaps in it

Parallel wave fronts approach the barrier. λ= h mv Most of the wave energy will be absorbed or reflected. λ = wavelength (metres) of the electron. h = Plank’s constant (= 6.63x10-34) -31 m = mass of the electron (= 9.11x10 kg) v = velocity of the electron, in ms-1.

The part of the wave which gets through a gap will act like a point source of waves. A semicircular wave pattern forms from each gap.
This is
Diffraction

Example Calculation
Find the wavelength of an electron which is
5
-1 travelling at a velocity of 4.35x10 ms .
Solution

λ= h mv You can see diffraction occur if you watch water waves enter a harbour or similar.

= 6.63x10-34/(9.11x10-31 x 4.35x105)
= 1.67x10-9 m
(1.67 nanometres)

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At this point you might think “so what?”
The “so what” is what happens AFTER diffraction occurs...
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Davisson & Germer’s Experiment

Diffraction Forms
Interference Patterns

Davisson and Germer used a modified cathode ray tube to test de Broglie’s hypothesis.

Once a set of waves have been diffracted, the 2
(or more) sets of spreading waves now meet each other and wave interference occurs:

A beam of electrons travelling through a vacuum was allowed to strike a crystal of nickel, specially prepared so that electrons would reflect from parts of it. Different parts of the beam could then overlap their pathways as they travelled into a detection device which could measure the intensity of the beam.

If the waves are “in phase” (crest matches crest) the waves add together for double the amplitude

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Result?
An interference pattern was detected! This proved that electrons have wave properties, and confirmed the de Broglie hypothesis.

Constructive interference If the waves are “out of phase” (crest matches trough) the waves cancel for zero amplitude

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=

Why Are the Bohr Orbits Stable?
A quick review of some important points:
Rutherford’s atomic model places electrons in orbit, but classical theory predicts they should constantly be emitting light because they are accelerating.

Destructive interference However, this isn’t happening, so Bohr proposes that there are “allowed”, stable orbits where electrons don’t constantly give off light. (They only radiate when they “jump” orbits)

If light waves are diffracted, then projected onto a screen, or captured on photographic film, an interference pattern appears... perhaps a line of light spots (where waves add together constructively) and dark zones (where waves are cancelling). The exact appearance of the pattern depends on the geometry of the “slits” and the wavelength of the waves.

Beam of light striking a barrier with slits in it

What makes these “allowed orbits” stable?

de Broglie’s particle-wave theory of the electron explains: Light falling on screen or photo film shows a pattern of light and dark spots

An allowed orbit is where the wavelength of the electron exactly fits to form a “standing wave” around the nucleus.

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Light spot where waves add together

“Standing waves” are a well-known wave phenomenon in which an exact number of full wavelengths can “resonate” or reverberate in a stable way. For example, all musical instruments involve standing waves of sound energy in a string or air space.

Dark zone where waves cancel The “allowed orbits” around an atom are located at distances from the nucleus which allow the quantum energy of the electron to fit in an exact number of wavelengths to form a standing wave.

Diffracting waves form
Interference Patterns

Can you guess what’s coming?

At any other distance, the orbit cannot fit a standing wave with an exact number of wavelengths, so the electron cannot exist there.

de Broglie has proposed an hypothesis that electrons may have wave properties.
What should a good scientist do?
Test the hypothesis by experiment, of course!

The electron is a particle, with mass and momentum. It is also a wave, with a wavelength λ (λ = h/mv) and capable of diffraction, interference and standing wave behaviour.
Welcome to the world of Quantum Physics!

How do you test for wave properties?
Test electrons to see if they show
Diffraction & Interference Patterns, of course!
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An electron forms a
“Standing
Wave” around the nucleus 7

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The Contributions of Heisenburg & Pauli
Before you leave the electron orbits and dive into the atomic nucleus, the syllabus asks you to assess the contributions of 2 other great scientists.

“If you think you understand
Quantum Theory... then you really don’t understand Quantum Theory!”

Werner Heisenberg (1901-76) was a German physicist who is best remembered for the
“Heisenberg Uncertainty Principle”, for which he was awarded the
Nobel Prize in 1932.
Heisenberg developed the mathematical framework for Quantum Mechanics. He showed that the dual nature of the “particle-wave” which describes the electron (and the light photon), makes it impossible to know everything about any particle at any moment. Either you know where it is, or you know how much momentum it has, but you cannot know both things at once with any certainty.
This “uncertainty” about things at the atomic scale was described by Heisenberg as mathematical probabilities. Thus an electron orbit becomes a “region of probability” in which there is a good chance (but not a certainty) that the electron exists.

Wolfgang Pauli (1900-58) was born in Austria, but became an American citizen. He is best remembered for the
“Pauli Exclusion Principle”, (Nobel Prize 1945) which states that 2 electrons in the same atom cannot have exactly the same quantum state.
His mathematical analysis established the idea that the Bohr-de Broglie orbits are just one of several different types of quantum properties that electrons can have.
This gives rise to the idea of “sub-orbits” within an atom (this explains the “hyperfine lines” in emission spectra) and shows why 2 electrons with almost the same quantum state, but opposite “spin” will tend to pair up. (Hence “Cooper Pairs”, and electron pairs in chemical bonding.)

This all sounds very airy-fairy, but its validity has been spectacularly confirmed by many experiments and phenomena such as the
“quantum tunnelling” effect, involved in semiconductor operation and electrical superconductivity. Later in this topic you will see that Pauli also made an important contribution to understanding nuclear processes as well.

An Assessment
In the 1920’s, Quantum Theory was being accepted as a “necessary evil” to satisfactorily describe the structure of an atom, and account for all the known observations.
However, the explanations being used were a mixture of new “quantum” ideas overlaid on a framework of “classical” Physics, so it was all rather artificial or contrived.
It was the theoretical work of Heisenberg & Pauli that built Quantum
Mechanics into a complete, new branch of Physics without the need for any reference to the “old” Physics.
Therefore, their contributions must be seen as being very important.
Although the details of their work are beyond the scope of this course, they allowed Physics to become a fully modern study with a complete theoretical base which can explain atoms, super-conductivity, semi-conductors, nuclear processes and even the creation of the Universe itself.
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Worksheet 2

Rutherford-Bohr Model of the Atom

Fill in the blank spaces

Student Name..........................................

Rutherford’s model of the atom:
• in the centre is a tiny, dense a).............................
• Electrons (discovered by b)................................) are in c)................................ around the outside.
The model had a major problem: theoretically, electrons which are d)................................ should constantly emit e)...................................., causing all matter to constantly f)....................... with light.

• Electrons can q).............................. from one orbit to another. When they do so they must
r)............................ or ..................................... an amount of energy. This energy difference relates to the s)................................ of a spectral line in accord with t)...........................’s Quantum
Theory and the u).................................. equation.
• Electrons in “v)............................... orbits” have a quantity of w)...................................... which is always a multiple of h/2π.

The “g).......................................................” of an element refers to the precise set of
h).................................... of light emitted if the element is energised, for example, in a
i).............................................................. The lines are visible if the light is viewed through a
j)...................................................

Bohr was able to link his idea to the Balmer
Series of hydrogen spectral lines. In fact, it is highly unlikely he could have developed his idea without this evidence.
However, the Bohr model had a number of limitations: • It worked only for x).............................................
• It could not explain the different
y)...................................... of the spectral lines.
• There was evidence from the “z).........................
Effect”, and the observed “aa).............................” spectral lines, that each orbit was actually ab)......................... ..................................................
The model could not explain these observations. The visible lines in the spectrum of
k)................................. had been named the
“l).................................
Series”, and the
m)........................................ equation had been formulated to calculate the n)................................. of each of the lines in the series.
Bohr used the evidence of the Balmer Series to refine
Rutherford’s atomic model. He suggested that:

• Electrons o)........................................................., in which they will not p).........................................

COMPLETED WORKSHEETS
BECOME SECTION SUMMARIES

Worksheet 3

de Broglie & Matter Waves

Fill in the blank spaces

Student Name..........................................
They detected an l).............................. pattern which proved that the electrons were undergoing m)................................. This proved that electrons do have n)..................... properties, and confirmed de Broglie’s hypothesis.

Louis de Broglie argued that if Einstein’s photons of light are waves with a)........................ properties, then electrons could be b)....................... with c)....................... properties.
He extended Bohr’s model to derive an equation for the d).............................. (wave measurement) of the electron. Bohr’s “allowed orbits” were explained as e)....................................... waves, with an integer number of f).................................. fitting exactly around that orbit.

o).............................. is a wave phenomenon in which waves which penetrate a small aperture, then act like a point source of waves and
p)........................ in a q).......................................... pattern. When waves from 2 (or more) apertures overlap, they r).................................... with each other. Where crest meets crest the waves
s)................... ........................... creating a higher
t).................................... wave. Where crest meets trough, the waves u)........................ each other.
With light, this results in a pattern of
v)......................... and ................................. spots.

De Broglie’s hypothesis had g).............................. impact on the scientific community. It seemed an interesting idea, but there was no
h)............................... from observations or
i)................................... to connect it to.
Two
scientists,
j)...........................
&
............................ carried out an experiment in which a beam of k)............................... was aimed at a crystal.

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Following the confirmation of de Broglie’s theory, the science of Quantum Mechanics was given a complete theoretical framework by the work of Werner w)....................................... and
Wolfgang x)...............................
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Worksheet 4

Test Questions

section 2

Student Name...............................
4.
Explain how de Broglie would describe Bohr’s
“allowed orbits” around the nucleus.

1.
Use de Broglie’s equation to calculate:
a) the wavelength of an electron with velocity
2.25x106 ms-1 (mass of electron = 9.11x10-31kg)

5.
a) What is diffraction?
b) the velocity of an electron if its quantum wavelength is 4.75x10-9m.

b) The diagram shows a breakwall with parallel water waves approaching. There are 3 boat channels through the wall. Complete the diagram showing the pattern of the waves which go through the boat channels.

c) Use the wave equation to find the quantum frequency of the electron in (b).

Water waves striking a breakwall with 3 boat channels

d) Use Plank’s equation to calculate the quantum energy of the electron in (b).

2.
Describe the impact of de Broglie’s proposal that particles could have wave properties.
Account for this reaction by the scientific community. 6.
Assess the contribution of Heisenberg & Pauli to the development of atomic theory.

3.
Outline the experiment of Davisson & Germer.
State the result of the experiment and explain the significance of this result.

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3. INTO THE NUCLEUS
Nucleons

Discovery of the Neutron

A “nucleon” means any particle located in the nucleus of an atom. We now know that there are 2 types of nucleon:

The existence of the neutron was proven in 1932 by James Chadwick (1891-1974).

Protons

It was impossible then to detect and measure neutrons directly. The method Chadwick used relied upon neutrons colliding with other particles, then applying the scientific principles of Conservation of Energy and Conservation of
Momentum to measure the properties of the neutron. Beryllium
Paraffin Wax

The existence of protons was considered likely almost as soon as the electron was discovered. By the 1920’s the proton had been positively identified, and its properties measured.

Neutrons

target

As early as 1907 it had been suggested that protons alone were not sufficient to account for the mass of most atoms. It was suspected that there must be another nucleon, with considerable mass, but no electric charge. However, it was 25 years before the neutron’s existence was proven.

α

Proton

Neutron

+1.602x10-19C

Mass

1.673x10

-27

kg

n0

+

p

Detecting equipment Radioactive substance emitting α-particles p

Contrasting the Properties of the Nucleons

Electrical
Charge

target

• The alpha (α) particles emitted by a radioactive substance were used to bombard a beryllium target. 0 (neutral)
1.675x10-27kg

• The beryllium emitted neutrons, which (having no electrical charge) are very penetrating and are unaffected by electric or magnetic fields, so could not be measured or studied directly. Other scientists had thought the radiation was gamma
( γ ) waves of extreme high energy.

Note that:
• The charge on a proton is exactly the same magnitude, but of opposite sign to that carried by an electron. • In a normal atom:
No. of protons = No. of electrons = “Atomic No.”

• Some of the neutrons then hit a second target of paraffin wax, which has a lot of hydrogen in it.
Occasionally a neutron collision would dislodge a proton.

• Protons and neutrons have almost identical masses. (The neutron is slightly heavier)
Both are almost 2,000 times heavier than an electron, so virtually all the mass of an atom is in the nucleus.
No.protons + No.neutrons = “Atomic Mass Number”

• Chadwick was able to study some of these protons and measure the energy they carried.

Thus we get the familiar atomic model, with electrons (in Bohr’s allowed orbits) around a nucleus of protons and neutrons.

• Chadwick could then apply the principles of
Conservation of Momentum and Energy to calculate the mass and velocity of whatever had hit the protons and dislodged them.

MAKE SURE YOU UNDERSTAND THE SHORTHAND DESCRIPTION

The results indicated the presence of a particle
(not γ-rays) with a mass almost the same as a proton, and no electric charge. This matched perfectly with the (then hypothetical) neutron, so the existence of the “missing” nucleon was confirmed. For example:
Sodium atom electrons = 11 protons = 11 neutrons = 12

Na
11
23

Background Information
Radioactivity had been discovered in 1896.
Although it was not fully understood, the use of α-particles as “atomic bullets” in experiments p had become quite routine.

Total nucleons = 23
(protons + neutrons)
Atomic Mass Number = 23

After Chadwick’s experiment, the neutron became the next “bullet” of choice.

Atomic Number = 11

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Transmutation

It would be wise to revise...

To “transmute” something means to change it into a different form or substance.

See Preliminary Topic “Cosmic Engine” to revise the properties of α, β & γ radiation.

In Nuclear Physics, “Transmutation” refers to an atom changing into an atom of a different element, by undergoing a nuclear reaction.

Transmutations occur during:
• radioactive decay of natural or artificial radioisotopes.
• nuclear fission in a nuclear power station, or “atom bomb”.
• nuclear fusion in the stars, and in a “hydrogen bomb”.

Radioactivity
Some naturally-occurring atoms have a nucleus which is unstable and will spontaneously undergo transmutation to change into a more stable form.
During the reaction, a variety of radiations are emitted from the nucleus.
There are several different reactions which can occur; knowledge of only the 2 most common reactions is required by the syllabus.

Beta ( β ) Decay

Alpha ( α ) Decay

Some atomic nuclei, of any size, have an unstable mix of protons and neutrons. If there is an excess of neutrons, a neutron can be turned into a proton plus an electron.

Alpha decay occurs in atoms which have a very large nucleus and are unstable. To achieve greater stability, the nucleus may spontaneously eject an alpha particle to carry away excess mass and energy.

1
0

Example:
Uranium is well known as a radioactive substance, and “nuclear fuel” for nuclear reactors and bombs. Its most common isotope is U-238, meaning it has a mass number of 238.
It decays as follows:
238

U
92

Uranium-238
2

234

Th
90

+

4
2

He

Alpha particle Thorium-234
2

Note that the Mass No. always decreases by 4, and the Atomic No. by 2

+ n n+ Gamma ray also emitted in most cases

88

Ra

86

Rn

+

4
2

He

14
6

Electron

Proton

C

14

N
7

Nitrogen

+

0
-1
1

e-

+

β-particle p γ
Gamma ray

Once again Transmutation has occurred.
+

In many cases of beta-decay there is a gamma ray emitted as well.

γ

Note that the Mass Numbers and Atomic
Numbers ALWAYS BALANCE across the equation. Hint: Use the Periodic Table to find Atomic
Numbers and identify names and symbols.
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-1
1

e-

The result is that:
• Number of neutrons decreases by 1.
• Number of protons increases by 1.
(This means Atomic Number goes up by 1 but Atomic Mass Number does not change)
• The electron is ejected from the nucleus at high speed. This is the Beta particle... a high speed electron.

Carbon

222

0

+

Example
Carbon-14 is a well-known radioisotope which decays: Example 2
Radium-226 transmutes by alpha decay:
226

p+

How can this happen? It seems like magic, but it shows what a strange place the quantum world is. Some detail on how such things can happen will be covered later; for now you must accept that it actually happens.

The α-particle p consists of
2 protons &
2 neutrons.
It is the nucleus of a Helium atom

The Uranium atom has
TRANSMUTED
into a different element

1

Neutron

γ

+

1

n0

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Pauli and the Neutrino
To have avoided detection, this hypothetical particle must have no mass (or so little that it was not measurable) and no electric charge.
However, it could carry quantum energy. Pauli’s idea was that there was a certain total energy involved in b-decay; some was carried off by the beta particle, the rest by the mystery particle.

It was known that the electrons ejected during Beta decay varied considerably in their velocity, and the amount of energy they carried. This was puzzling, because it was thought that the process involved was the same in every β-decay, so why did the energy vary?

Enrico Fermi did the mathematics and the whole scenario worked so well in theory that the scientific community accepted the new particle, even though it was not positively detected and identified until 1956.

In 1931, Wolfgang Pauli suggested a quantum explanation.
What if there was another particle being produced, that no-one had detected?
This “missing” particle could carry away some of the energy in varying amounts. neutron

n

proton

β-particle p (electron)

This new particle was eventually christened the “neutrino” (little neutral one) and is now a totally accepted fact of the sub-atomic quantum world. In fact, there are a whole family of neutrinos; to keep it simple (KISS
Principle!) the one released in beta decay is an “anti-neutrino”.

The sum of the energy of the beta particle and neutrino always adds up to the same amount.

The symbol used for the anti-neutrino is
ν. The full equation for a beta decay is therefore: 14

anti neutrino 6

C

Carbon

14
7

N

Nitrogen

+

0
-1
1

e-

+

ν

+

γ

Gamma antiβ particle neutrino

What Holds the Nucleus Together?
This question had been asked as soon as
Rutherford had proposed that atoms have a nucleus. There were just 2 forces then understood, which could be operating in the nucleus:

Since the nucleus does exist, and doesn’t instantly explode, it was realized that there must be another force operating. It was called simply the “Strong Nuclear Force”.

Gravity

Its properties could be inferred and calculated:
• It must be much stronger than the protonproton electrostatic repulsion. (it’s over 100X stronger) All masses attract all other masses by gravity.
This would attract all nucleons to each other.

Electrostatic Forces

• It must be independent of charge and attract all nucleons... protons & neutrons.

All charged particles exert a force on other charged particles. This force would not act on neutrons, but should cause protons to be repelled by other protons.

• It must be extremely short-ranged, operating only across the tiny distances of the nucleus.
(Otherwise it might cause neighbouring atomic nuclei to fuse together, and eventually pull all matter into one lump!) Even before its existence was proven, the Strong Nuclear Force was known to exist, and scientists began speculating on how to tap into its enormous energy potential...

Calculations showed that the electrostatic repulsion would be much, much stronger than gravity. The nucleus should instantly fly apart!

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Measuring Mass & Energy in the Nucleus
Before going any further, you need to know about the commonly used methods of measuring mass and energy at the atomic level.

Mass in Atomic Mass Units

Energy in Electron-Volts

The “atomic mass unit” (u) is a measure of mass devised for convenience in Chemistry. Roughly speaking, both a proton and a neutron have a mass of 1 u, although in the calculations following, you need to be much more precise.
Obviously, 1 u is a very small mass:

The “electron-volt” (eV) is an energy unit that is convenient because the energy of sub-atomic particles has traditionally been measured by their behaviour within electric fields.

-27

1 u = 1.661x10

1 eV is the energy gained by an electron accelerating in an electric field with a potential difference of 1 volt.

1 eV is an extremely small amount of energy:

kg

1 eV = 1.602 x 10-19 joules of energy

You need to be able carry out calculations using either unit, so the following data may be useful.

Proton
Mass (in kg)

1.673x10-27

Mass (in u)

1.0073

so the unit often used is the mega-electron-volt
(MeV)
1 MeV = 1x106 (one million) eV

Neutron
1.675x10-27

This is convenient when dealing with individual atoms or particles.

1.0087

Mass Defect in the Nucleus
It was realized that incredibly powerful forces were operating within the atomic nucleus. How could such forces arise?

Example Calculation
A normal carbon atom contains 6 protons and 6 neutrons. (also 6 electrons, but mass is negligible)
The nucleus is known to have a mass = 11.9967 u
= 1.993x10-26 kg
Calculate the Mass Defect, and total Binding Energy.

The answer lies in the fact that the mass of every atomic nucleus (except hydrogen ) DOES
NOT ADD UP.

Solution

If you add up the mass of all the protons+neutrons in any nucleus,

In kg and joules

In u and MeV

Mass of 6 protons
= 6 x 1.673x10-27
= 1.004x10-26 kg

the total is always more than the actual measured mass of the whole nucleus.

Mass of 6 protons
= 6 x 1.0073
= 6.0438 u

Mass of 6 neutrons
Mass of 6 neutrons
= 6 x 1.675x10-27
= 6 x 1.0087
-26
= 1.005x10 kg
= 6.0522 u
Total particle mass
Total particle mass
-26
= 2.009x10 kg
= 12.0960 u
∴ Mass defect
∴ Mass defect
-26
-26
= 2.009x10 - 1.993x10
= 12.0960 -11.9967
= 1.600x10-28kg
= 0.0993 u

Mass of
Mass of
Protons + Neutrons > Whole Nucleus
This difference is called the “Mass Defect”. It’s as if a little bit of mass “went missing” when the protons and neutrons joined together to form the nucleus.

These are the same, just different units

Where is the missing mass?
It has converted to energy...

E = mc2

This missing mass has converted to binding energy according to

(you should have known that Einstein would be involved sooner or later!)

E = mc2
= 1.6x10-28 x (3.00x108)2
= 1.44 x10-11J

...to provide the “Binding Energy” of the Strong
Nuclear Force which holds the nucleus together. These are the same, just different units

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Each 1 u converts to
931.5 MeV of energy
(This value is in your
Physics Data Table)
So, binding energy
= 0.0993 x 931.5
= 92.50 MeV

From here on, all calculations will be done in atomic mass units (u) and MeV.

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The Manhattan Project

Nuclear Fission

Following a “letter of concern” (outlining the danger of nuclear research in Nazi Germany) from Einstein to the President of the USA , the top secret “Manhattan
Project” was set up in 1942. Its objective was to research nuclear fission and develop an “atomic bomb” if this was possible.

In the 1930’s, it was discovered that bombarding
“target” atoms with alpha particles could occasionally produce a transmutation to a new radioactive isotope.
27
13

4

Al +

2

30

He

15

α-particle

Aluminium

P +

new isotope of phosphorus

1
0

n

The first step was to discover if a self-sustaining chain-reaction of fissions was possible. Enrico Fermi was appointed the leader of the scientific team. He designed the reactor or “nuclear pile”, which was built in a squash court at the University of Chicago.

neutron

In Italy, brilliant young physicist Enrico Fermi (190154) decided that using neutrons as “atomic bullets” would be even more productive.

In December 1942 the reactor achieved the first selfsustaining, controlled chain reaction.

In 1934 he began bombarding every possible element, in turn, with neutrons and studying the resulting radioactivity to detect any new radioisotopes. Over 40 were discovered very quickly. For example:
19
9

F

+

Fluorine

1

20

n
0

9

The Fission Chain Reaction
Since fission is set off by a neutron, and since it releases more neutrons, it follows that a chain reaction can occur, in which each atom which splits can set off more.

F

New, previously unknown radioisotope of Fluorine

Neutron

In one experiment he bombarded uranium atoms with neutrons, confidently expecting to produce atoms of
“transuranic” elements. The radiation “signatures” detected were unexpected and puzzling, but he was focused on other things and failed to investigate further. Start

Fermi had “split” the nucleus, but it was another 4 years before other scientists in Germany confirmed what had happened. In his sample of uranium were atoms of U-235 which had absorbed a neutron, then totally disintegrated:
92
36
235
92

U+

Uranium

Kr

1

3

n
0

Neutron

Krypton isotope 141
56

Ba

1
0

Barium isotope n

3 extra neutrons released.
These can set off other atoms in a
“chain
reaction”

This is Nuclear Fission; the splitting of the nucleus., with enormous energy release, due to a mass defect and E=mc2.

In a critical mass of “fissile” atoms, if every fission sets off (say) 2 more, then the chain reaction grows exponentially within a fraction of a second. This is uncontrolled fission, and results in a nuclear explosion of devastating power... an “atomic bomb”.
If a neutron-absorbing material (such as cadmium) is present, it is possible to absorb many of the neutrons so that each fission sets off exactly one other. This is controlled fission and is what Fermi achieved in his
“pile” in 1942, and what occurs in every nuclear power station.

Meanwhile, Fermi had continued on with his work, and was awarded the Nobel Prize of 1938 for his production of new radioactive materials.
With war looming in Europe and a Fascist regime in
Italy, Fermi and his Jewish wife used attendance at the Nobel Prize ceremony in Sweden to flee to the
USA, where Fermi was immediately accepted into the scientific community.

There are only 2 nuclei which will readily undergo fission: 239
235
Pu
U
94
92
Plutonium-239 which can
Uranium-235
which be made from U-238 by occurs naturally in neutron bombardment in uranium ores, but in a nuclear reactor. very small amounts.

By then he was aware of nuclear fission and its huge energy potential, and that the experiments confirming fission had been done in Nazi Germany. On the eve of
World War II, it seemed that the knowledge to develop an “atom bomb” was in the hands of the enemy.
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If the amount of “fissile” atoms is below a certain “critical mass”, most neutrons escape without striking another nucleus, and the s chain reaction is not self-sustaining and dies down.

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Mass Defect During Nuclear Fission
The enormous energy released by nuclear fission is due to a “mass defect” between the starting nucleus and the product nuclei.
Photo by
Daron Cooke

For example, in the fission of Uranium-235:
(Note: fission products can vary)
235
92

U+

U-235
2
mass
235.0439 u

1
0

n

neutron mass 1.0087 u

148
57

La +

La-148
1
mass
147.8114 u

Total Mass before
Fission
236.0526 u

85
35

Br + 3

Br-85
8
mass
84.8917 u

1
0

n

3 neutrons mass 3.0261 u

Total Mass after
Fission
235.7292

Mass Defect = (Mass Reactants - Mass Products)

This is the amount of energy generated by an average size power station in about 30 years.

= 236.0526 - 235.7292 = 0.3234 u
Energy yield per fission:
Remember that
1u
of mass

The energy released might seem a very small amount, but this is from just one atom.
In (say) 10kg of uranium there are about 2.5x1025 atoms.
Simulated
If all of these were to
Nuclear
undergo fission, the
Explosion
total energy released would be about 1x1015 joules, all released in a split second, in the case of an atom bomb.

This is the plutonium fission bomb, nicknamed “Fat Boy”, which destroyed the city of Nagasaki in 1945.

931.5 MeV of energy

So, energy released = 0.3234 x 931.5
= 301.2 MeV
(This equates to about 5 x 10-11 joules of energy)

Practical Work

Observing Nuclear Radiations
You may have done practical work with one or more methods of detecting and observing radiation from a radioactive isotope.

Enrico Fermi in 1943 working on the “Manhattan
Project”

The Wilson Cloud Chamber is a simple device which allows the “trails” of alpha particles to be seen.
Simple School
Cloud Chamber
Small chip of radioactive material

When you add up the total mass of all the products of a fission reaction, it is less than the starting mass.

The tracks of alpha particles appear as thin
“condensation
trails”

The chamber is cooled with “dry ice” so that the vapours within are on the point of condensation.
If a source of alpha particles is placed inside the chamber, tiny “tracks” can be seen. An alpha particle collides with air molecules and ionises millions of them along its path. The ionised molecules serve as sites of condensation, so a visible “condensation trail” briefly shows the path of each alpha particle.

This “mass defect” has been converted to energy.
E = mc2
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Worksheet 5

Into the Nucleus

Fill in the blank spaces

Student Name..........................................

Beta decay occurs when a neutron converts to a x)............................... An
y).......................... is created as well, and it is ejected from the nucleus at high speed... the beta particle. The Atomic
Number
z).......................................... while the Mass Number aa)...............
................. ..................

A “nucleon” refers to all the particles
a)......................................., and includes
b)........................ & ..................................
These are different in their properties in that c).......................... are slightly heavier, and d)........................... carry
e)................ electric charge.
The existence of the neutron had been suspected, and was finally proven by
f)...................................... in 1932. When
g)...............-particles were smashed into a beryllium target a penetrating radiation was produced. Others had thought it was h)........................ rays.
Chadwick allowed this radiation to strike a second target of i)..........................
This
dislodged
j)............................ which he could detect and measure their energy. By applying the principles of k)..............................
................................. he could calculate the properties of the “mystery radiation”. His results indicated a
l).............................. with mass similar to
m).................... but without n)...................
...............................

It was discovered that the beta particles from different isotopes carried ab).................................... .......................
Pauli suggested this was because ac)........................................................... which shared the energy with the electron. This particle is an ad)................
...........................
The nucleus is held together by the
“ae)................................................” which has to be much more powerful than the af)....................................... between protons. It acts only over ag)........................ distances, and attracts all ah)......................... to each other. The force arises from the “Mass ai).........................” of the nucleus. A small amount of the mass has been aj)........................ ................... according to ak).................................(equation)

“Transmutation” refers to an atom
o)..................................................... when it undergoes a p)............................... reaction. This can occur during
q)....................................... decay, or during nuclear r).......................... or
............................. (opposite processes).

Nuclear al).......................... occurs when a nucleus is struck by a am)............................., and then an).................. ................. It also releases
2 or 3 more ao)................................ which can cause a ap)............................
Reaction to occur. During each fission there is a large energy release due to aq)............................................................. Alpha decay occurs in a nucleus which is unstable because s)....................
................................ It ejects an alpha particle (which is made up of t)................
......................................) so that the Mass
Number u)...................................... and the Atomic Number v)....................
........................ There is usually emission of w)............................. as well.

The first controlled fission reaction was achieved in 1942 as part the secret
“ar).................................... Project”. The reactor was designed by as).................................................. COMPLETED WORKSHEETS
BECOME SECTION SUMMARIES
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Worksheet 6

Practice Problems

Nuclear Reactions
Alpha Decay Equations

Beta Decay Equations

Work out the missing nuclide, identifying
• Mass Number & Atomic Number
• Symbol & name

1. If each of the following nuclides underwent beta decay, write the symbol, Mass Number &
Atomic Number of the new nuclide.

1.

222

Rn
86

Student Name..........................................

4

+

2

He

+

γ

a) Iodine-131
b) Thorium-234

2.

3.

241

Am
95

210
84

+

Po

+

4
2

4
2

He

+

He

+

γ

c) Hydrogen-3
d) Sodium-24

γ

e) Uranium-239
4.

233

5.

210

Pa
91
Po
84

+

4
2

+

4
2

He

+

γ

f) Cobalt-60

He

+

γ

2. Write complete decay equations for the beta decay of:
a) Lithium-8

b) Xenon-135
6. Write the equation for the alpha decay of
Actinium-227
c) Phosphorus-31
7. Write the equation for the alpha decay of
Plutonium-244
d) Chlorine-38

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Worksheet 7

Practice Problems

Mass Defect

Student Name..........................................

Use the data table at right.

Data for Calculations

For each of the following nuclear reactions calculate: a) the Mass Defect (u)
b) the energy released (MeV)

Nuclide

1.

9
4

Be +

4
2

12

He

6

C +

1
0

1

22
11
92
36
141
56
235

235
92

U+

1

n
0

141
56

Ba +

92
36

92

Kr + 3

1
0

7

9.0122
21.9780

Kr

91.8804

Ba

4

4.0026

Na

9

1

Be

2

1.0087

He

4

2.

Nuclide

n

0

n

Nuclear Mass
(u)

140.8167

U

235.0439

H

1.0073

Li

7.0160

1
3

12

C

11.9967

Mg

24.9575

Sr

91.8776

Ba

144.8115

Pu

239.0446

6
25
12
92
38
145
56
239
94

Nuclear Mass
(u)

n
4.
239
94

3.

Pu +

145

1

n
0

56

Ba +

92
38

1

Sr + 3 0 n

5.

7

Li +
3

1
1

H

4
2

He +

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4
2

22

He

11

19

Na +

4
2

He

25
12

Mg +

1
1

H

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Worksheet 8

Test Questions

section 3

1.
Outline Chadwick’s experiment to confirm the existence of the neutron, and discuss the importance of
“conservation laws” in determining the neutron’s mass.

Student Name...............................
4.
Discuss why the neutrino was
“invented” (and by whom) and its existence accepted, many years before it was physically detected and proven to exist. 2.
Account for the need for the “strong nuclear force” and outline its properties. 5.
a) Explain why a “chain reaction” of fissions is possible.

3.
a) What is meant by the “mass defect” of the nucleus?
b) Compare the requirements for controlled and uncontrolled nuclear fission. b) Explain the connections between the strong nuclear force, the mass defect, and Einstein’s equivalence of mass & energy. HSC Physics Option Topic “From Quanta to Quarks”
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4. APPLICATIONS OF NUCLEAR PHYSICS
Significance of the
Manhattan Project

Photo of
Horoshima a few days after the bomb.
Parts of the city literally “ceased to exist”.

Fermi’s first controlled fission chain reaction in 1942 was just the first step in one of the most significant scientific research projects in human history.
Within 3 years, fission bombs were used to destroy the Japanese cities of Hiroshima and Nagasaki and bring a sudden end to World War II.
The Manhattan Project brought the world into the
“Atomic Age”, with the following significant changes:
This ruined building in
Horoshima,
Japan, has been preserved as a memorial to the many thousands who died in the atom bomb attacks in 1945

Technologies Developed
• Nuclear power stations, currently meet about 20% of the world’s energy needs. Fission power is
“Greenhouse friendly”, but presents the danger of devastating accidents such as at Chernobyl (Ukraine) in 1986. There are also great challenges in the safe storage and disposal of radioactive wastes from fission power stations.
• Nuclear weapons proliferated during the 40 year
“Cold War”. On several occasions the world seemed to be on the brink of a nuclear war which potentially could have destroyed all human civilization.

Later in this section are more examples, and specific details, of technologies which are based on Nuclear
Physics and are therefore a direct result of the
Manhattan Project.

• Rockets were developed to deliver the nuclear weapons, but the “spin-off” was their use for space exploration and satellite technology. The modern world relies heavily on satellites for communication, commerce and finance as well as entertainment.

Nuclear Technologies have been widely considered as having more risks and dangers than benefits.
However, there have also been many “spin-offs” which have been highly beneficial to society.
Whatever your opinion, the Manhattan Project was certainly one of the most significant scientific research events in human history.

• Nuclear Medicine includes all the ways that nuclear technology is used for diagnosis and treatment of a wide range of health problems, including cancer.
• Even the humble smoke alarm in your home is connected to nuclear technology. It contains a tiny pellet of radioactive material (Am-241) manufactured in a nuclear reactor.

As always, the Science (and the technology it leads to) is neither good nor bad; that is determined by the choices and decisions made by people.

Nuclear Physics is Still Investigating Matter
Project, and the “Nuclear Age”
Particle Accelerators

The Manhattan all grew from research by scientists like
Chadwick and Fermi who wanted to find out about the structure of atoms. They used alpha particles and neutrons as “bullets” to probe the nucleus to try to understand the fundamental structure of matter.

are another tool of modern research.
A Particle Accelerator uses powerful electromagnets to accelerate electrically charged particles through huge circular tubes. Other electromagnets “steer” and focus the beam of accelerating particles. At the desired energy level, the particles are allowed to collide head-on, or smash into their target. An array of detection equipment studies the particle tracks and radiation from the collision.

Well, guess what? Scientists are still doing exactly that, and still using (essentially) the same technique.

Neutrons as Nuclear Probes

For example, the accelerator at C.E.R.N.
(underground on the French/Swiss border) is 27 km in circumference, and accelerates particles to velocities of 99.995% of the speed of light.

Neutrons are still used as probes because their lack of electric charge allows them to penetrate the nucleus more easily than a proton or alpha particle. A beam of neutrons might be scattered by a nucleus, or other particles may be ejected from it. This allows scientists to study the structure of the nucleus.
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At the end of the section is a brief summary of our understanding of matter, as revealed by the “atom smashers”. 21

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Nuclear Fission Reactors
The main peaceful use of nuclear fission technology is to operate controlled chain reactions in a fission reactor, and use the energy released to make electricity.
There are many different designs. The following schematic diagram shows the main features of all fission power stations
Moderator

(usually graphite or “heavy water”)
The reactor “pile” is made of a moderator substance which slows down the neutrons. This increases the likelihood of each neutron causing a fission in the next nucleus it hits.
(fast neutrons tend to pass through without causing a fission)

Control Rods are made of cadmium or boron which absorbs neutrons.
Lowering them into the pile slows the chain reaction; raising them speeds it up.
In an emergency, they can be dropped under gravity to shut the reactor down.

Steam driven
Turbine
&
Generator

Fuel Rods

Uranium or Plutonium
Each rod is less than the critical mass, but together they form well over the critical mass needed to sustain a chain reaction.

Heat
Exchanger
Heat from reactor boils water to steam Electricity

Each rod can be withdrawn for re-fuelling f

Condenser
These are usually huge cooling towers

Heat absorbing fluid (Often a liquid metal)
Circulates through the pile and transfers heat to the heat exchanger for steam production.

Sizewell Nuclear Power Station, England

The reactor “pile” is inside this dome, heavily shielded to prevent any radiation escaping

Photo by
Les Powell

The following is background information only...

Instead, we rely on hydro-electricity and on burning fossil fuels. Most of our electricity is made by burning coal, which is a major contributor to the “Greenhouse
Effect” and Global Warming.

Australia is a non-nuclear country.
We have one small fission reactor in Sydney for research, and to produce radio-isotopes for medicine and industry.

Many people believe that nuclear technologies have been improved, and are now safe enough for Australia to look towards nuclear power for our growing energy demands.

Ironically, Australia is also the country with the largest mineral deposits of uranium ores. Our economy benefits greatly by selling uranium to other nations, but our government policy (based on the democratic will of the people) has always been NOT to use nuclear power.
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Please have an opinion on this important issue, but make sure it is an informed opinion.
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Uses of Radio-isotopes in Medicine

Radio-isotopes in Industry
The gamma rays from cobalt-60 are very penetrating, and very destructive to living cells.

One application of Nuclear Physics that is likely to affect each of us, or our family, is the use of radioisotopes in health care.

In the manufacture of medical supplies, such as bandages and dressings, it is vital that the product is totally sterile (germ-free). This is achieved by irradiating the products with doses of gamma radiation high enough to destroy any bacteria or fungi spores which might be present.

Radio-isotopes are used for:

Imaging and Diagnosis
Radio-isotopes have now joined X-rays and ultrasound scans for medical imaging and diagnosis.
For example, the artificial isotope thallium-201 is used with a “gamma ray camera” to image heart muscle and detect any damage from heart disease.
When injected into the bloodstream, thallium tends to collect in any active muscle because it “mimics” potassium ions. Being radioactive (it gives off a lot of low-energy gamma rays) it allows a gamma ray camera to make computer-aided images of heart muscle to identify if any part of it is damaged.
The isotope has an extremely short half-life, so it rapidly disappears and presents little danger to the patient. In paper manufacture, alpha emitting isotopes such as Americium-241, are used for thickness control. A radiation detector constantly measures the percentage of radiation which penetrates the paper as it moves at high speed through “thicknessing” rollers. If the radiation level drops, this means the paper is too thick, so the rollers are automatically adjusted.

Cancer Treatment
“Radiation therapy” relies on the fact that rapidlydividing cancer cells are more easily killed by gamma radiation than normal healthy cells.
The isotope cobalt-60 (which emits beta and strong gamma radiation) is commonly used as a source of radiation which is accurately beamed into the tumour.

Radio-isotopes in Engineering
In aircraft construction, the airplane parts may be welded together. It is essential that the welded joints are totally strong and free of defects. X-rays are not able to penetrate the metal welds, but gamma rays can.

Another example is the use of iodine-131 in the treatment of thyroid cancer. The thyroid gland is located in the throat, and produces a vital hormone which has iodine atoms in it.
This gland is the only part of the body which uses iodine, and enzymes in the gland are able to chemically “recognize” iodine ions and very efficiently “harvest” iodine from the blood stream. To “see” inside the weld, gamma rays (again, cobalt-60) are used like X-rays; they are beamed through the welded joint and an image captured by a “gamma-ray camera”. Analysis of the image allows engineers to be sure of the quality of the welding.

Iodine-131 is radioactive and emits beta and gamma rays.

Radio-isotopes in Agriculture

If a small amount of I-131 is injected into a patient who has a tumour in the thyroid gland, the radiation level is so low that there is little risk to their healthy tissue.

Location of
Thyroid
Gland

Radio-iosotopes are not used directly in farming, but are very important in Agricultural research, such as that carried out by the CSIRO.
For example, to study and compare the rates of uptake of fertilisers into crop plants, isotopes such as nitrogen-15 and phosphorus-32 are commonly used.

However, due to the chemistry of the iodine, the thyroid gland rapidly absorbs the isotope and concentrates it.
The radiation is concentrated in the “target organ” and is very effective in destroying the tumour.

Small concentrations of these isotopes can be included in a fertiliser applied to experimental plants. The uptake of the fertiliser, and where it ends up in the plant, can be “traced” by using radiation detection equipment. This research ultimately helps farmers to produce food crops more efficiently and economically.

I-131 has a short half-life and the radiation disappears rapidly. HSC Physics Option Topic “From Quanta to Quarks”
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The “Standard Model” of Matter
After 100 years of scientific research into the sub-atomic quantum universe, just what is the latest “picture” we have for the structure of matter?
Our modern understanding is known as the “Standard Model”, and is a description of both matter and energy (since these are inter-changeable) at its most fundamental level.

The Four Fundamental Forces:
Gravity (the weakest of all) acts between all masses, and holds planets, stars & galaxies together and in orbit.
Electomagnetic Force

acts only between charged particles. It is responsible for holding atoms and molecules together (all chemical bonds are basically electrical) as well as causing all electrical and magnetic phenomena. The Nuclear Weak Force

is involved in radioactivity such as when an electron and an anti-neutrino are produced during beta decay in the nucleus.

The Nuclear Strong Force (the strongest of all) acts only between particles of the “hadron” family. It acts only over very short range and is what holds protons and neutrons together in the atomic nucleus.
We now know that protons & neutrons are composed of smaller particles called quarks.

So far, it has NOT been possible to combine Quantum Mechanics and the
Standard Model of Matter with
Einstein’s Relativity Physics.
This would be the GUT; “Grand United
Theory”, which would combine an explanation of EVERYTHING.

The Structure of Matter
Many Particles, but Just Two Families.
Once the “atom-smashing” Particle
Accelerators were developed, scientists began detecting a bewildering assortment of sub-atomic particles.
This confusion has now been simplified with the realisation that all these particles belong to just 2 basic types or classes:

Leptons

&

Hadrons

Leptons

include the electron, and the neutrino family.(there are several types of neutrino)
As well as being the particles which flow in an electric current, electrons are at home in orbit around a nucleus. Remember too, that they have wave properties and form (de Broglie’s)
“standing waves” within
(Bohr’s) allowed orbits.

Hadrons are made from QUARKS
Hadrons include the proton and neutron, and a family of particles called mesons.

Then there are the

All the hadrons are composed of combinations of “quarks”.

These are quantum “particlewaves” and are the means by which all the particles exert forces on each other.

Each quark has a charge of either +2/3 or -1/3
(compared to the charge of an electron = -1).

Bosons

The best known is the “photon” of electromagnetic radiation,
Protons contain 3 quarks with charge = +2/3 +2/3 -1/3 = +1 such as light.
When formed in the nucleus Neutrons contain 3 quarks with charge= +2/3 -1/3 -1/3 = 0 during beta decay, the
Gravity is thought to involve electron (and an antiQuarks themselves come in a variety of “flavours” which have been given whimsical names such as “charm” and “gravitons”, but these have not neutrino) is instantly ejected yet been proven to exist.
“strange”. These names are labels for quantum states and at high speed. bear no connection to the normal meanings of these words.
The nuclear forces are carried by gluons (strong force) and
W-particles (weak).

Anti-Particles and Anti-Matter
It has been discovered that for every Hadron and Lepton that exists, there is also a corresponding anti-particle.
For example, there are electrons, and there are anti-electrons (“positrons”) which have the same mass, but opposite electric charge. There are also anti-protons, anti-neutrons, and so on. As you know, the other particle formed in beta-decay is an anti-neutrino.
Theoretically, there could exist “anti-matter” with atoms made entirely of anti-particles.
When any particle and its anti-particle meet, they mutually annihilate each other... all the mass is converted into energy (photons of gamma radiation) according to E=mc2.
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Worksheet 9

Applications of Nuclear Physics

Fill in the blank spaces
The Manhattan Project brought the world into the a).......................... Age and was one of the b)............................... scientific research projects in history. It led to technologies such as c)......................................... from which the world gets about 20% of its electricity. d)....................................... were a threat to civilization during the
“e)............................ War”. Rockets were developed to carry weapons, but now we rely on them for f)........................
................................. The many uses of
g)............................
substances in Medicine and Industry are also direct
“spin-offs”.

Student Name..........................................

Nuclear reactors not only provide electricity, but are used to make many artificial u)............................... isotopes that are useful in Medicine and Industry.
Medical uses include v)............................. and diagnosis, as well as treating
w)..................... by irradiation. An isotope used for imaging is x)............................., while y)........................ radiation for cancer therapy often comes from the isotope z).............................
This same isotope is also used in industry, for example, to aa)...................................... surgical dressing and bandages after manufacture and packaging. In paper manufacture, the isotope ab).................... is used to control the thickness by measuring the penetration of ac).............................. through the paper.

Nuclear research is still going on.
Neutrons are excellent “probes” or
“bullets” because h)..................................
................. In addition, i).......................
................................. are used to accelerate j)............................... particles up to near the
k)..................
............................ From the l)....................
& .................... from a collision, scientists are able to infer the structure of matter.

In engineering, gamma rays from ad)......................... are used to check the quality of ae).........................................., for example in aircraft construction.
In agricultural research, isotopes such as af)...................... and ............................. are used to “trace” the movement of chemicals into and through a plant.

A nuclear fission reactor has 3 main components: • Fuel Rods made of a “fissile” material such as m)................................. or
...................................
• n)........................ Rods (made of
o).......................) These control the rate of fission by absorbing p).........................
• The Moderator, which is usually
q)................................. or “heavy water”.
Its job is to r).................................... the neutrons so that fission is more likely to occur. The energy released by the fission reaction is used to make steam, which then drives a s)............................. and ............................. to make
t)...........................

Our modern “picture” of matter is called the ag)................... ..............................
There are many sub-atomic particles, but they all belong to 2 classes:
• ah)........................, including the electron and a variety of ai)......................
• aj)..........................., including the ak)....................... and ............................
Each of these is composed of smaller
(although more massive) particles called al)...........................

COMPLETED WORKSHEETS
BECOME SECTION SUMMARIES

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Worksheet 10

Test Questions

section 4

1.
Assess the significance of the
Manhattan Project to society, including mention of 2 technologies that were developed from it.

Student Name...............................

4.
Using named examples of 4 different radio-isotopes, describe an application of radioactivity in
a) medicine.

b) industry.

c) engineering.
2.
Explain the basic principles of a fission reactor, outlining the composition and function of the fuel rods, moderator and control rods.

d) agriculture.

5.
Discuss the the key features of the
“Standard Model” of matter including the main “classes” of particles, examples of each, and whether each is composed of anything smaller.

3.
a) What properties of neutrons make them useful as “probes” to investigate the nucleus?

b) Identify and briefly describe another technology used in modern nuclear research to investigate the structure of matter. HSC Physics Option Topic “From Quanta to Quarks”
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CONCEPT DIAGRAM (“Mind Map”) OF TOPIC
In all the Core Topics you were given examples of a “Mind Map” as a way to summarise the content of the topic.
If you have found this a useful way to summarise and learn, then you may want to do it again.
By now you should have developed the skills to do it yourself...

Rutherford & Bohr
Models of the Atom de Broglie
&
Matter Waves

FROM QUANTA
TO QUARKS
Into the
Nucleus
Applications of Nuclear
Physics

HSC Physics Option Topic “From Quanta to Quarks”
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Answer Section
Worksheet 1
1.

2

7.

2

1 = RH( 1/nf - 1/ni ) λ = 1.097x107( 1/12 - 1/82 ) λ 1/λ = 1.080 x 107
∴ λ = 9.20x10-8 m ( = 92 nm)
Visible light has wavelengths from about 400-700 nm.
This is much shorter, therefore is in the ultra violet.

Electrons in orbit around central nucleus Atom mostly empty space
Nucleus

Worksheet 2

2.
The existing theory for EMR stated that electrons accelerating in circular motion should constantly emit light energy, but obviously they don’t.

a) nucleus
b) J.J.Thomson
c) orbit
d) accelerating/in circular motion
e) (electromag) radiation f) glow
g) emission spectrum
h) wavelengths
i) discharge tube
j) spectroscope
k) hydrogen
l) Balmer
m) Rhydberg
n) wavelength
o) revolve only in “allowed” orbits
p) radiate energy/emit light
q) jump
r) absorb or emit
s) wavelength/frequency t) Plank’s
u) Rhydberg
v) allowed
w) angular momentum x) hydrogen
y) intensities/brightness z) Zeeman aa) hyperfine ab) divided into sub-orbits

3.
a) Balmer Series is the 4 lines of visible light in the emission spectrum for hydrogen.
b)
1 = RH( 1/nf2 - 1/ni2 ) λ = 1.097x107( 1/22 - 1/42 ) λ 1/λ = 2.057 x 106
∴ λ = 4.86x10-7 m λ c) c = λ.f, ∴ f = c/λ
= 3.00x108 /4.86 x10-7
= 6.17x1014Hz.
E = h.f
= 6.63x10-34 x 6.17x1014
= 4.09x10-19 J.
d) The energy difference between the 2nd and 4th quantum levels (or “allowed orbits”).

Worksheet 3
a) particle
c) wave
e) standing
g) very little
i) experiment
k) electrons
m) diffraction
o) Diffraction
q) semi-circular
s) add together
u) cancel
w) Heisenberg

4.
It is very unlikely that Bohr could have developed his atomic model without the evidence of the hydrogen spectrum. The fact that there were distinct lines at precise wavelengths all pointed to quanta of energy, rather than variable amounts.
5.
a) More energy, because it is the difference between
5th-2nd orbits, compared to 4th-2nd.
b) Higher frequency, because Plank’s E = hf shows a direct relationship between energy and frequency.
c)Shorter, because frequency and wavelength are inversely related by the wave equation , v=lf.
6.
a)
• electrons revolve only in certain stable, “allowed orbits” • Energy must be absorbed, or emitted, in quantised amounts when an electron jumps from one orbit to another. • Within the “allowed orbits” the electron’s angular π momentum is quantised to a multiple of h/2π.
b)
* it applied only to the hydrogen atom.
* it could not explain the different intensities of the spectral lines.
* it could not explain the “hyperfine” spectral lines.
* it could not explain the “Zeeman Effect”.

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b) particles
d) wavelength
f) wavelengths
h) evidence
j) Davisson & Germer
l) interference
n) wave
p) spread out
r) interfere
t) amplitude
v) bright and dark
x) Pauli

Worksheet 4
1.
a) λ = h = 6.63x10-34/(9.11x10-31 x 2.25x106) mv = 3.23x10-10 m
b) λ = h λ mv so v = h/mλ
= 6.63x10-34/9.11x10-31x4.75x10-9
= 1.53x105 ms-1. λ c) c = λf, so f = c/λ = 3.00x108/4.75x10-9
= 6.32x1016 Hz
d) E = h.f
= 6.63x10-34 x 6.32x1016
= 4.19x10-17 J.

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Worksheet 4 (cont)

z) increases by 1 aa) stays the same ab) different amounts of energy ac) another particle was produced ad) anti-neutrino ae) Strong Nuclear Force af) electrostatic repulsion ag) extremely short ah) nucleons ai) defect aj) converted to energy ak) E = mc2 al) fission am) neutron an) splits apart ao) neutrons ap) chain aq) mass conversion/defect ar) Manhattan as) Enrico Fermi

2.
His proposal had very little impact at first. It was a
“neat” idea, and mathematically valid, but the scientific community took little notice because there was no evidence from observation or experiment to link it to. It was not until the hypothesis was tested by
Davisson and Germer that the Physics world really took notice.
3.
Outline: In a vacuum tube, a beam of cathode rays
(electrons) were beamed at a specially prepared nickel crystal.
Result: They detected an interference pattern in that part of the beam that reflected from the crystal.
Significance: this proved that electrons showed wave properties (diffraction & interference) and confirmed de Broglie’s hypothesis.

Worksheet 6
1. 218 Po
2.
84

237
93

Polonium

4.
The “allowed orbits” are where the the electron can exist as a standing wave around the nucleus. The orbit circumference is exactly equal to an integral number of electron wavelengths.

4. 237

5.
a) When waves pass through a small gap in a barrier, the gap acts like a point source of waves, which spread out in a semi-circular pattern.
b)

6. 227
89

Np

93

3. 206

Np

Lead

Neptunium

214

5.

Pb

82

Rn

86

Radon

Neptunium

223

Ac

Fr

87

+

4
2

He

+

γ

He

+

γ

Francium

7.

240

244

Pu
94

U

92

+

4
2

Uranium

Beta Decay Equations
1.

Xe

54

6.
In the 1920’s, Atomic Physics was using a mixture of
“classical” ideas, overlaid with the new quantum ideas, but it was artificial and contrived.

e) 239

24

d)

12

It was Heisenberg (“Uncertainty Principle”) and Pauli
(“Exclusion Principle”) who developed the theoretical framework of Quantum Mechanics so it could become a coherent, modern scientific model of matter.

91

93

Pa
Np

3

c)

f)

He

2
60
28

Ni

2.

a)

8

Li

3

b) 135

Worksheet 5

54

a) in the atomic nucleus b) protons & neutrons
c) neutrons
d) protons
e) positive
f) Chadwick
g) alpha
h) gamma
i) paraffin wax
j) protons
k) conservation of momentum and energy
l) particle
m) a proton
n) electric charge
o) changing into a different element
p) nuclear
q) radioactive
r) fission or fusion
s) too large
t) 2 protons & 2 neutrons
u) decreases by 4
v) deceases by 2
w) gamma rays
x) proton
y) electron
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b) 234

Mg

a) 131

c) 31
15

d) 38
17

29

Xe

P
Cl

8

Be

4

135
55
31
16
38
18

0

e-1
1

+

Cs

+

S

+

Ar

+

0

e-1
1
0

+
+

ν ν +

γ γ +

e-

+

ν

+

γ

e-1
1

+

ν

+

γ

-1
1
0

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Worksheet 7

4.
It was noticed that the electrons produced by beta decay varied a lot in the energy they carried, although the process was thought to be the same in each case.
Why?
Pauli suggested that there was another particle involved, which shared the total energy with the electron... the neutrino (actually an anti-neutrino).
This explanation of beta decay was so convincing that the existence of the neutrino was accepted many years before its actual detection.

1.
Mass defect = (mass reactants) - (mass products)
= (9.0122+4.0026)-(11.9967+1.0087)
= 13.0148-13.0054
= 0.0094 u
Energy release = 0.0094 x 931.5 = 8.756 MeV
2.
Mass defect = (mass reactants) - (mass products)
= (235.0439+1.0087)-(140.8167+91.8804+3.0261)
= 236.0526 - 235.7232
= 0.3294 u
Energy release = 0.3294 x 931.5 = 306.8 MeV
3.
Mass defect = (mass reactants) - (mass products)
=(7.0160+1.0073)-(4.0026 x 2)
= 8.0233 - 8.0052
= 0.0181 u
Energy release = 0.0181 x 931.5 = 16.86 MeV
4.
Mass defect = (mass reactants) - (mass products)
=(239.0446+1.0087) - (144.8115+91.8804+3.0261)
= 240.0533 - 239.7180
= 0.3353 u
Energy release = 0.3353 x 931.5 = 312.3 MeV
5.
Mass defect = (mass reactants) - (mass products)
=(21.9780+4.0026) - (24.9575+1.0073)
= 25.9806 - 25.9648 = 0.0158 u
Energy release = 0.0158 x 931.5 = 14.72 MeV

5.
a)A fission reaction is set off by a neutron striking a suitable nucleus. The fission process produces 2 or 3 new neutrons, each of which can set off another fission. Therefore, once started, it is possible to have a chain reaction of fissions.
b) If 2 or more neutrons are released, and each sets off another fission, the chain reaction will grow exponentially. This is an uncontrolled reaction.
If some neutrons are absorbed so that each fission sets off exactly 1 other fission, then the chain reaction will continue, but at a steady, controlled rate.

Worksheet 9
a) Atomic/Nuclear
b) most significant
c) nuclear power stations
d) Nuclear weapons
e) Cold
f) launching satellites
g) radioactive
h) their lack of electric charge makes it more likely they will collide with the nucleus
i) particle accelerators j) charged
k) speed of light
l) radiation & particles
m) uranium or plutonium
n) Control
o) cadmium/boron
p) neutrons
q) graphite
r) slow down
s) turbine & generator t) electricity
u) radioactive
v) imaging
w) cancer
x) thallium-201
y) gamma
z) cobalt-60 aa) sterilise ab) americium-241 ac) alpha particles ad) cobalt-60 ae) welded joints af) nitrogen-15 & phosph-31 ag) Standard Model ah) leptons ai) neutrinos aj) Hadrons ak) proton & neutron al) quarks

Worksheet 8
1.
Chadwick used a radioactive material to fire alpha particles at a beryllium target. This produced a penetrating radiation that others thought were gamma rays. Chadwick let this radiation strike a paraffin wax target. From this came streams of protons, dislodged by the “mystery” rays. He used the laws of conservation of energy and momentum to calculate the nature of the radiation that had dislodged the protons.
This showed it was particles with mass about 1u, and no electric charge... neutrons.
2.
Calculations showed that gravity was too weak to hold the nucleons together in the face of electrostatic repulsion between protons. No other forces were known, but there must exist another force in the nucleus. This “Strong Nuclear Force” must attract all nucleons, and must be very powerful. It must be extremely short-ranged, and work only across the distance of a single nucleus.

Worksheet 10
1.
This was one of the most significant scientific projects in history. It led directly to the development of nuclear weapons which (during the Cold War) threatened to destroy civilization, and still have that potential. It also lead to nuclear technologies such as the many uses of radioactive isotopes in Medicine (eg for imaging, diagnosis & cancer treatment) Both these technologies, and others, have had profound impacts upon society, both positive and negative.

3.
a) Every nucleus larger than hydrogen has a mass slightly less than the sum of the protons and neutrons it contains. The difference is the mass defect. b) The “missing mass” of the mass defect is mass that has converted to energy according to E=mc2.
This energy provides the “binding energy” of the strong nuclear force.

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Worksheet 10 (cont)

4.
a) Iodine-131 can be used to treat thyroid cancer.
Iodine becomes concentrated in the thyroid gland where the radiation kills tumour cells with minimal damage to healthy tissue.

2.
The fuel rods are composed of uranium or plutonium which undergoes fission. Each rod is below the critical mass for a chain reaction, but when many rods are inserted into the reactor, a chain reaction can be sustained.

b) Americium-241 is used to monitor the thicknes of paper during manufacture. The penetration of alpha particles through the paper is used as a measure of thickness, and equipment adjusted automatically.

Control rods are made from cadmium or boron and are good neutron absorbers. These control the rate of the reaction by adjusting how many neutrons are available to continue the chain reaction.

c) Gamma rays from cobalt-60 can be used to “image” welded joints in aircraft manufacture.

The moderator is graphite or “heavy water” which slows the neutrons down. This makes collisions more likely to set off a fission, and allows the reactor to run efficiently at a steady rate.

d) Nitrogen-15 is used as a “tracer” in agricultural research. Added to soil or fertilizer, its uptake and travel through the plant can be traced by radiation detection equipment.

3.
a) Neutrons have no electrical charge. This makes them more penetrating, and less likely to be deflected by electrons or protons before they collide with a nucleus. 5.
There are many sub-atomic particles, but they all belong to 2 classes:
Leptons include the electron, and a variety of neutrinos. These are fundamental particles, not composed of anything smaller.

b) Particle Accelerators use powerful electromagnets to accelerate charged objects up to very high speeds.
They are then allowed to collide head-on, or to strike
“target” atoms. The radiation and particle tracks from the collision are studied to reveal information about the structure of matter.

Hadrons include the proton and neutron and others.
These are composed of combinations of different quarks. A proton, for example, is composed of 3 quarks, bound together by a huge mass defect.

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