Blackbody Radiation A Spectroscopic Study
Blackbody radiation: a spectroscopic study
John Greavu
Partner: Nicholas Souhleris
TA: Yilikal Ayino (Friday, Section 006)
April 18, 2014
I. PRELAB
A blackbody is a body that absorbs all electromagnetic radiation and emits a continuous spectrum, such as heated cavern with just a small opening to the outside world. In 1900, German physicist Max Planck derived an expression for this blackbody spectrum. Knowing that oscillators emit radiation, he assumed that oscillators within the cavern were responsible for the emissions. In a discovery that launched quantum physics, Planck discovered that only integer multiples of the oscillators natural frequency v multiplied by a constant (his own – h) are capable of producing electromagnetic radiation (i.e. hv, 2hv, 3hv, etc. ).
The average energy of a quantum harmonic oscillator as a function of temperature T is given by
where k is Boltzmann’s constant. If we take into account density of states, and the fact that wavelengths between can be in the cavern, the energy per area per time, or the intensity, as a function of wavelength and temperature is given by
as v = c / . One can then show that this intensity spectrum has a peak at that is inversely proportional to the temperature and has a value of 2.898 x 10-3 meters/T (Kelvin) — this is Wien’s displacement law. If one were to integrate over all possible wavelengths, an equation for the total power P radiated by an area A as a function of temperature would be produced:
where is the Stefan-Boltzmann constant and the energy of the blackbody in question. The purpose of this experiment is prove the above equation, which states that power scales with the temperature to the fourth power, and to determine h or hc/k. The variation with temperature of the blackbody spectrum emitted by a tungsten filament in an incandescent light bulb will be measured. Although, we will not have a thermometer the temperature of the filament can still be determined by noting that the
John Greavu
Partner: Nicholas Souhleris
TA: Yilikal Ayino (Friday, Section 006)
April 18, 2014
I. PRELAB
A blackbody is a body that absorbs all electromagnetic radiation and emits a continuous spectrum, such as heated cavern with just a small opening to the outside world. In 1900, German physicist Max Planck derived an expression for this blackbody spectrum. Knowing that oscillators emit radiation, he assumed that oscillators within the cavern were responsible for the emissions. In a discovery that launched quantum physics, Planck discovered that only integer multiples of the oscillators natural frequency v multiplied by a constant (his own – h) are capable of producing electromagnetic radiation (i.e. hv, 2hv, 3hv, etc. ).
The average energy of a quantum harmonic oscillator as a function of temperature T is given by
where k is Boltzmann’s constant. If we take into account density of states, and the fact that wavelengths between can be in the cavern, the energy per area per time, or the intensity, as a function of wavelength and temperature is given by
as v = c / . One can then show that this intensity spectrum has a peak at that is inversely proportional to the temperature and has a value of 2.898 x 10-3 meters/T (Kelvin) — this is Wien’s displacement law. If one were to integrate over all possible wavelengths, an equation for the total power P radiated by an area A as a function of temperature would be produced:
where is the Stefan-Boltzmann constant and the energy of the blackbody in question. The purpose of this experiment is prove the above equation, which states that power scales with the temperature to the fourth power, and to determine h or hc/k. The variation with temperature of the blackbody spectrum emitted by a tungsten filament in an incandescent light bulb will be measured. Although, we will not have a thermometer the temperature of the filament can still be determined by noting that the