MChem Master of Chemistry Master of Chemistry: Physical Chemistry 2

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?

Accepted Answer

9 times higher

Answer

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?

Accepted Answer

The operator postulate

Answer

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:

Accepted Answer

There is a change in dipole moment during the vibration

Answer

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:

Accepted Answer

½hν

Answer

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:

Accepted Answer

2J+1

Answer

Each rotational level J has 2J+1 degenerate M_J substates ranging from −J to +J.

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Practice Test

MChem Master of Chemistry Master of Chemistry: Physical Chemistry 2