Quantum Mechanics

Quantum Mechanics Additional Practice Problems

Which energy diagram in the figure below is appropriate for each of the following situations?

I. Vibrational states of a diatomic molecule such as O 2
II. Idealized quantized spring - mass oscillator
III. Electronic, vibrational, and rotational states of a diatomic molecule such as O2
IV. Electronic states of a single atom such as hydrogen

1. I-C, II-A, III-B, IV-C
2. I-C, II-B, III-D, IV-A
3. I-A, II-C, III-D, IV-B
4. I-A, II-D, III-A, IV-C
5. I-A, II-B, III-D, IV-C
6. I-B, II-A, III-C, IV-D
7. I-B, II-D, III-C, IV-A
8. I-B, II-C, III-A, IV-D
9. I-D, II-C, III-A, IV-B
10. I-D, II-B, III-A, IV-C

Watch Solution

Consider the spacing of vibrational energy levels of Pb and Al based on the quantum harmonic oscillator model for the interatomic bound. Pb has a stiffness of ks ∼ 5N/m and an atomic mass of 207 mN (where mN is the mass of a nucleon). For Al, the stiffness is ks ∼ 17N/m, and the atomic mass is 27 mN. Determine the ratio of the energy level spacings, ΔEAl / ΔEPb. Choose one:

1. 0.5

2. 1

3. 6

4. 1.33

5. 2

6. 5.11

7. 3.33

8. 4

Watch Solution

The wave function of a particle is shown in the figure below. What is the probability of finding the particle at x1? Assuming the wave function is symmetric, what is the probability of finding the particle at any position between 0 and x2?

Watch Solution

For a hydrogen atom in the 3 p state. what is the value of the smallest possible angle between the angular momentum vector and the z-axis?

(a) 90°

(b) 45°

(c) 35°

(d) zero

(e) none of the above

Watch Solution

The number of 3d states (the number of distinct sets of quantum numbers) for hydrogen is

(a) 32

(b) 18

(c) 14

(d) 10

(e) 8

(f) 5

(g) 4

(h) 2

(i) none of the above

Watch Solution