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

1. What is the maximum kinetic energy (in eV) of a photoelectron when a surface, whose work function is 5.0 eV, is illuminated by photons whose wavelength is 400 nm? (A) 3.1 (B) -1.9 (C) 1.9 (D) 0 (E) 1.2

2. How much energy is in an 89.7-MHz photon of FM radiation?(Hint: The Planck constant is h = 6.626 × 10⁻³⁴ J·Hz⁻¹ = 4.135 × 10⁻¹⁵ eV·Hz⁻¹) (A) 2.2 × 10⁻³³ J (B) 5.9 × 10⁻²⁷ J (C) 7.4 × 10⁻⁴² J (D) 9.5 × 10⁻²⁶ J (E) 3.7 × 10⁻²⁵ J

3. The experimental observation(s) below that require(s) a quantum explanation for the photoelectric effect (A) is that more photoelectrons are emitted when the light frequency increases. (B) is that the maximum kinetic energy of the photoelectrons is related linearly to the frequency of the light. (C) is that every metal surface has a work function, a minimum amount of energy needed to free electrons. (D) is that the stopping potential measures the kinetic energy of the photoelectrons. (E) are all of the above.

4. An electron is accelerated through a potential difference of 25 000 V. What is the de Broglie wavelength of the electron (in m)?(Hint: the electron mass is me = 9.11 × 10⁻³¹ kg and 1 eV = 1.602 × 10⁻¹⁹ J) (A) 7.8 × 10⁻¹² (B) 6.8 × 10⁻¹² (C) 6.5 × 10⁻¹² (D) 5.9 × 10⁻¹² (E) 5.5 × 10⁻¹²

5. Because the factor ℏ on the right side of Heisenberg's uncertainty principle has units of joule-seconds, it suggests that the energy of a system also has uncertainty. The uncertainty in energy depends on the length of the time interval during which a system exists. ΔEΔt ≥ ℏ/4π. Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is me/100 (me = 9.11 × 10⁻³¹ kg). How long will this particle exist? (A) 8.1 × 10⁻¹⁹ s (B) 2.3 × 10⁻²³ s (C) 1.0 × 10¹⁵ s (D) 1.2 × 10¹³ s (E) 6.4 × 10⁻²⁰ s

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)

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