CHM2330 Midterm Exam 1 Review
CHM2330 (Winter 2015)
Midterm # 1 Review
Short answer questions - 9
Long answer questions - 15
Possible bonus questions - 5
Short Answer Questions:
1) Draw the Maxwell Distribution graph, with all axis labeled as well as descriptions of each curve.
2) What does the correspondence principle state?
3) What is the ultraviolet catastrophe? What is one of the consequences of the ultra violet catastrophe?
4) What does the de Broglie hypothesis state?
5) Write down the integrals which describe orthonormal wavefunctions.
6) What is the general definition of complementary operators in terms of their commutation properties?
7) How many nodes does the wavefunction of the 1st excited state of a 1D particle in a box have?
8) Rank the following from least to greatest, root-mean-squared speed, mean speed, and most probable speed. >
9) Describe Graham’s empirical law of effusion.
>
Long Answer Questions:
1) The mean speed for a pure unknown ideal gas at an unknown temperature is 212.0cms-1.
i) What is the root-mean-square speed? ii) The most probable speed?
2) Determine the degeneracies of the first four energy levels for a particle in a three-dimensional CUBE.
Show your reasoning for full marks.
3) Consider a particle on a 2D ring which is described by the (UNNORMALIZED) wavefunction.
Ψ?? (?) = ? ????
a) Find the normalization constant for this wavefunction.
b) Is the wavefunction an eigenfunction of the rotational angular momentum operator? If so, give the eigenvalue. 4) Determine the wavelength of the most intense electromagnetic radiation emitted from a furnace at
2500.1 centigrades. (Hint: Use Wien’s law)
5) Calculate the speed of a neutron of wavelength 3.0nm. (Mass of neutron: 1.675 x 10^-27 kg)
6) Suppose that the wavefunction for a system is:
1
1
3 + √2?
?(?) = ?1 (?) + ?2 (?) +
?3 (?)
2
4
4
and that all ?(?) are normalized eigenfunctions of the kinetic energy operator, with eigenvalues E1, 3E1 and 7E1, respectively.
a) Verify that ?(?) is
Midterm # 1 Review
Short answer questions - 9
Long answer questions - 15
Possible bonus questions - 5
Short Answer Questions:
1) Draw the Maxwell Distribution graph, with all axis labeled as well as descriptions of each curve.
2) What does the correspondence principle state?
3) What is the ultraviolet catastrophe? What is one of the consequences of the ultra violet catastrophe?
4) What does the de Broglie hypothesis state?
5) Write down the integrals which describe orthonormal wavefunctions.
6) What is the general definition of complementary operators in terms of their commutation properties?
7) How many nodes does the wavefunction of the 1st excited state of a 1D particle in a box have?
8) Rank the following from least to greatest, root-mean-squared speed, mean speed, and most probable speed. >
9) Describe Graham’s empirical law of effusion.
>
Long Answer Questions:
1) The mean speed for a pure unknown ideal gas at an unknown temperature is 212.0cms-1.
i) What is the root-mean-square speed? ii) The most probable speed?
2) Determine the degeneracies of the first four energy levels for a particle in a three-dimensional CUBE.
Show your reasoning for full marks.
3) Consider a particle on a 2D ring which is described by the (UNNORMALIZED) wavefunction.
Ψ?? (?) = ? ????
a) Find the normalization constant for this wavefunction.
b) Is the wavefunction an eigenfunction of the rotational angular momentum operator? If so, give the eigenvalue. 4) Determine the wavelength of the most intense electromagnetic radiation emitted from a furnace at
2500.1 centigrades. (Hint: Use Wien’s law)
5) Calculate the speed of a neutron of wavelength 3.0nm. (Mass of neutron: 1.675 x 10^-27 kg)
6) Suppose that the wavefunction for a system is:
1
1
3 + √2?
?(?) = ?1 (?) + ?2 (?) +
?3 (?)
2
4
4
and that all ?(?) are normalized eigenfunctions of the kinetic energy operator, with eigenvalues E1, 3E1 and 7E1, respectively.
a) Verify that ?(?) is