6. The expectation value of a function f(x) of x when the wave function depends only on x is given by ⟨f(x)⟩ =
(A)
(B)
(C)
(D)
(E)

7. The graph below shows the value of the probability density |ψ(x)|² in the region -3.00 m ≤ x ≤ +3.00 m. The value of the normalization constant A is (A)(B)(C)(D)(E)

8. What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy is 2h²/mL²? (A) 2 (B) 4 (C) 8 (D) 1 (E) 16

9. The wave function for a particle in a box of length L is given by ψ(x) =. If the box extends from x = 0 to x = L, what is the probability of finding the particle between x = 0.60L and x = 0.70L? (A) 0.05 (B) 0.20 (C) 0.25 (D) 0.10 (E) The probability is not given.

10. A particle in a finite potential well has energy E, as shown below.The wave function in region I where x ＜ 0 has the form ψI = (A)(B)(C) A sin(kx) (D) B cos(kx) (E) A sin(kx) + B cos(kx)

11. Classically, the concept of "tunneling" is impossible. Why? (A) The total energy of a particle is equal to the kinetic and potential energies. (B) The velocity of the particle would be negative. (C) The kinetic energy of the particle would be negative. (D) The kinetic energy must be equal to the potential energy. (E) The total energy for the particle would be negative.

12. The ground state energy of a harmonic oscillator is (A) E = ℏω (B) E = ℏω/4 (C) E = (2/3)ℏω (D) E = 0 (E) E = ℏω/2

13. Rutherford's experiment, in which he fired alpha particles of 7.7-MeV kinetic energy at a thin gold foil, showed that nuclei were very much smaller than the size of an atom because (A) some alpha particles passed through the foil undeflected. (B) some alpha particles were deflected backwards. (C) some alpha particles were captured by the gold nuclei. (D) the alpha particles could not get closer than 10⁻¹⁰ m to the gold nuclei. (E) the alpha particles split into deuterium nuclei when they encountered the gold nuclei.

14. An electron in a hydrogen atom makes a transition from the n = 4 to the n = 3 energy state. Determine the energy (in eV) of the emitted photon. (A) 0.54 (B) 1.51 (C) 0.85 (D) 0.66 (E) 10.2

15. How fast is the electron moving in the first Bohr orbit? (A) 3.3 × 10⁶ m/s (B) 5.5 × 10¹⁵ m/s (C) 4.4 × 10⁶ m/s (D) 5.5 × 10⁶ m/s (E) 2.2 × 10⁶ m/s

16. Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = ℓℏ. Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector is . Which one, if either, is correct, and why? (A) Ruth, because the maximum value of L is (B) Ruth, because the orbital angular momentum always lines up with a magnetic field so that has its maximum value along the field. (C) Zeke, because the maximum magnitude of L is = ℓℏ. (D) Zeke, because the orbital angular momentum always lines up with a magnetic field so that has its maximum value along the field. (E) Neither, because they have interchanged the maximum magnitude of , and ℓℏ, its maximum projection along a magnetic field direction.

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