MChem Master of Chemistry Master of Chemistry: Physical Chemistry 2 — Questions and Answers
Question 1: The time-independent Schrödinger equation for a particle in a one-dimensional box of length L gives quantized energies. What is the energy of the n=3 level relative to n=1?
- 3 times higher
- 6 times higher
- 9 times higher (Correct answer)
- 27 times higher
Correct answer: 9 times higher
Energy levels scale as n², so E₃/E₁ = 3²/1² = 9.
Question 2: Which postulate of quantum mechanics states that every observable corresponds to a Hermitian operator whose eigenvalues are the possible measurement outcomes?
- The superposition postulate
- The Born postulate
- The operator postulate (Correct answer)
- The collapse postulate
Correct answer: The operator postulate
The operator postulate assigns a Hermitian operator to each physical observable, with real eigenvalues as measurable values.
Question 3: In IR spectroscopy, a vibrational mode is IR-active only if:
- The molecule is nonlinear
- There is a change in polarizability during the vibration
- There is a change in dipole moment during the vibration (Correct answer)
- The molecule has a center of inversion
Correct answer: There is a change in dipole moment during the vibration
IR activity requires a change in the electric dipole moment during the vibration to couple with the oscillating IR electric field.
Question 4: The zero-point energy of a quantum harmonic oscillator with frequency ν is:
- 0
- hν
- ½hν (Correct answer)
- ³∕₂hν
Correct answer: ½hν
The ground state (n=0) energy of a harmonic oscillator is ½hν, called the zero-point energy.
Question 5: For a rigid rotor, the rotational energy levels are given by E_J = BJ(J+1). The degeneracy of level J is:
- J
- 2J
- 2J+1 (Correct answer)
- J(J+1)
Correct answer: 2J+1
Each rotational level J has 2J+1 degenerate M_J substates ranging from −J to +J.
Question 6: The Born-Oppenheimer approximation in molecular quantum mechanics assumes that:
- Electron spin is negligible
- Nuclear and electronic motions can be separated due to mass differences (Correct answer)
- All bonds are harmonic
- Relativistic effects are negligible for light atoms
Correct answer: Nuclear and electronic motions can be separated due to mass differences
Because nuclei are ~1836 times heavier than electrons, electrons adjust instantaneously to nuclear positions, allowing separation of their wavefunctions.
Question 7: The Heisenberg uncertainty principle states that Δx·Δp ≥ ħ/2. If the positional uncertainty of an electron is halved, the minimum momentum uncertainty:
- Halves
- Doubles (Correct answer)
- Quadruples
- Remains unchanged
Correct answer: Doubles
Since Δx·Δp ≥ ħ/2, halving Δx requires Δp to at least double to satisfy the inequality.
MChem Master of Chemistry Master of Chemistry: Physical Chemistry 2
The time-independent Schrödinger equation for a particle in a one-dimensional box of length L gives quantized energies.
What is the energy of the n=3 level relative to n=1?