True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 177.

(a) | α | > | β | (b) | α | = | β | (c) | α | < | β |

(a) L = 0.25 nm (b) L = 0.61 nm (c) L = 2.10 nm (d) L = 10.6 nm (e) L = 109 nm

A particle of unknown mass is in a 1-dimensional box of width L = 3.0 × 10^{-10} m with infinitely high potential walls at x = 0 and at x = L and zero potential for 0 < x < L. The particle is in the second excited state of the box.

What is the de Broglie wavelength λ of the particle?

(a) λ = 1.0 × 10^{-10} m (b) λ = 2.0 × 10^{-10} m (c) λ = 3.0 × 10^{-10} m (d) λ = 6.0 × 10^{-10} m (e) Not enough information is given.

(a) only at x = L/6 and x = 5L/6 (two values of x) (b) only at x = L/4 (one value of x) (c) only at x = L/6 and at x = L/2 and at x = 5L/6 (three values of x) (d) The probability is everywhere the same. (e) Not enough information is given.

How many distinct (n,l,m) states of the hydrogen atom with n = 3 are there? Neglect electron spin.

(a) 1 distinct state (b) 5 distinct states (c) 9 distinct states

(a) They are all equal to -1.51 eV. (b) The highest (most positive) energy is equal to -1.51 eV, the others are all smaller. (c) At least one energy is equal to -2.44 eV. (d) At least one energy is equal to +3.55 eV. (e) States with larger l have higher energies.

A particle is in a bound energy state of the finite depth potential well shown.

If we measure the particle's position in the well, which is the more likely result?

(a) The particle has a larger wavelength in the left half of the well. (b) The particle has a larger wavelength in the right half of the well. (c) The particle wavelength is the same on both sides of the well.

(a) at x = 0 (b) at x = L (c) The energy is the same everywhere.

(a) λ = 188 nm (b) λ = 300 nm (c) λ = 500 nm (d) Every λ ≤ 1000 nm can be absorbed. (e) No shorter wavelengths can be absorbed.

(a) Increase E_{1}, keeping E_{2} constant. (b) Increase |E_{2} - E_{1}|. (c) Increase a, keeping b constant. (d) Increase |b - a|. (e) none of the above

An electron is confined to an infinite 1-dimensional well of width L = 1.5 nm. At t = 0 it is in a superposition of the ground state and second excited state: Ψ(x,t=0) = aΨ_{1} + bΨ_{3} , where Ψ_{1} and Ψ_{3} are individually normalized.

What is the frequency of oscillation f of the spatial probability density?

(a) f = 1.27 × 10^{14} Hz (b) f = 2.54 × 10^{14} Hz (c) f = 3.24 × 10^{14} Hz (d) f = 3.55 × 10^{15} Hz (e) f = 2.29 × 10^{15} Hz

(a) a = b = 1/√2 (b) a = b = 1/2 (c) a = √(2/3), b = √(1/3) (d) a = √(2/3), b = -√(1/3) (e) No values of a and b will ever result in a zero probability density at the middle of the well.

(a) P_{3} = 1.00 (b) P_{3} = 0.399 (c) P_{3} = 0.518 (d) P_{3} = 0.841 (e) P_{3} = 0.917

The work function (energy needed to remove an electron) of gold is 5.1 eV. Two pieces of gold (at the same potential) are separated by a distance L.

For what value of L will the transmission probability for an electron to cross from one to the other be T ≈ 10^{-3}? Assume that G = 1 in the formula for the tunneling probability.

(a) L = 0.001 nm (b) L = 0.02 nm (c) L = 0.1 nm (d) L = 0.3 nm (e) L = 4 nm

(a) T ≈ 10^{-6} (b) T ≈ 0.5 × 10^{-3} (c) T ≈ 1 × 10^{-3} (d) T ≈ 2 × 10^{-3} (e) T ≈ 0.03

An electron is confined in a 3-dimensional rectangular box (V = 0 inside and V = ∞ outside) with sides L = 4 nm, 4 nm and 5 nm. What minimum energy E must a photon have in order to excite the electron out of its ground state. (The electron absorbs the photon.)

(a) E = 0.015 eV (b) E = 0.045 eV (c) E = 0.071 eV (d) E = 0.125 eV (e) E = 0.241 eV

(a) none (b) 1 (c) 2 (d) 4 (e) all 10

(a) <KE> = <KE_{0}> (b) <KE> = 2 <KE_{0}> (c) <KE> = 4 <KE_{0}>

(a) 0 (the atom does not recoil when it emits a photon) (b) 3.26 m/s (c) 121.6 m/s

You are sitting 10 meters from a musician (left-most dot) playing an instrument with a steady note at some unknown frequency f. You are facing in a direction perpendicular to the direction of the musician, as shown in the figure below (not to scale).

The speed of sound in air is 346 m/sec, while the speed in your head depends on whether the sound propagates directly across (i.e., through your brain, with diameter 15 cm), at v_{brain} = 1540 m/s, or propagates around the periphery through the skull bone (assumed to be spherical for this problem) at v_{skull} = 4080 m/s. Assuming the individual intensities from these two paths are the same, for what frequency will there be destructive interference at your left eardrum?

(a) f = 12.6 kHz (b) f = 8.3 kHz (c) f = 2.3 kHz

The intensity that each musician produces at your right eardrum when they play alone is 2 W/m^{2}. What is the net intensity, I, at your right eardrum? The intensity that each musician produces at your right eardrum when they play alone is 2 W/m^{2}. What is the net intensity I at your right eardrum?

(a) I = 0 W/m^{2} (b) I = 0.8 W/m^{2} (c) I = 1.5 W/m^{2} (d) I = 6.2 W/m^{2} (e) I = 7.0 W/m^{2}

By approximately what factor would we have to increase the HST mirror aperture to resolve the lunar rover left by the Apollo 11 astronauts under the most optimistic circumstances? Use a wavelength of 700 nm for the light being detected by the HST and require that we need to resolve 15 cm features in order to identify it.

(a) factor = 10 (b) factor = 100 (c) factor = 1000 (d) factor = 10000 (e) factor = 100000

(a) θ_{min} = 1° (b) θ_{min} = 2° (c) θ_{min} = 4° (d) θ_{min} = 8° (e) θ_{min} = 16°

In a two-slit interference experiment, a viewing screen is placed 5 meters directly behind two slits separated by 4 μm. Coherent, monochromatic light of wavelength λ = 700 nm emerges (in phase) from the slits. (Assume the slit width is very small compared to the wavelength λ.)

At what value of x on the screen does the largest-order intensity maximum occur (i.e., the one that is the farthest from the center line)?

(a) x = 1.2 m (b) x = 4.4 m (c) x = 5.0 m (d) x = 9.0 m (e) x = 15.7 m

(a) The separation decreases. (b) The separation increases. (c) There is no change.

Consider doubly ionized Lithium (Li^{++}), which has 1 electron orbiting a charge +3 nucleus.

Compare a_{o,Li} the most likely distance for the electron in a Li^{++} atom to be from the nucleus, with a_{o,H} the most likely distance for the electron in a hydrogen atom to be from the nucleus, assuming the electron is in the ground state in both cases. Which of the following is true?

(a) a_{o,Li} < a_{o,H} (b) a_{o,Li} = a_{o,H} (c) a_{o,Li} > a_{o,H}

(a) λ_{max} = 0.665 nm (b) λ_{max} = 10.1 nm (c) λ_{max} = 21 nm (d) λ_{max} = 137 nm (e) λ_{max} = 487 nm

(a) An ideal metal conducts because each electron 'belongs' to every nucleus in the crystal lattice, while in an ideal insulator, each electron is localized to a single nucleus. (b) Metals conduct much better than insulators because, per gram of material, metals have orders of magnitude more electrons. (c) At sufficiently low temperatures, (intrinsic) semi-conductors are effectively insulators.

(a) (4, 0, 0) (b) (4, 1, -1), (4, 1, 0) and (4, 1, 1) (c) (5, 2, +1) and (5, 2, -1) (d) all of the above (e) none of the above

(a) E_{quantum dot} / E_{molecule} = 1 (b) E_{quantum dot} / E_{molecule} = 6/5 (c) E_{quantum dot} / E_{molecule} = 5/3 (d) E_{quantum dot} / E_{molecule} = 15/2 (e) The information given is not sufficient to answer this question.

(a) Δf = 7 MHz (b) Δf = 14 MHz (c) Δf = 28 MHz

An electron is moving in the potential U(x) shown to the right. This potential is an even function of x. The energies, E_{1} = -1.5 eV and E_{2} = +0.5 eV, of the two lowest energy states are indicated by the dashed lines. Five x values are labeled A-F in the figure. Ψ_{1}(x) is the wave function of the ground state, and Ψ_{2}(x) is the wave function of the first excited state.

Which one of the following statements is not true?

(a) Ψ_{1}(A) = Ψ_{1}(F) (b) Ψ_{2}(A) = -Ψ_{2}(F) (c) Both Ψ_{1} and Ψ_{2} are proportional to sin(kx) in the regions A < x < B and D < x < F (though 'k' might be different for Ψ_{1} and Ψ_{2}) (d) dΨ_{1}/dx = 0 at x = C (e) d|Ψ_{2}|^{2}/dx > 0 for x < A

(a) Ψ_{1} (b) Ψ_{2} (c) They are the same.

(a) f = 4.8 × 10^{14} Hz (b) f = 3.6 × 10^{14} Hz (c) f = 1.24 × 10^{14} Hz

The graph at the right shows the results of a photoelectric effect experiment in which the stopping voltage was measured for several frequencies of light. The slope of the line is 4.0 × 10^{-15} volts/Hz, and the x-intercept is f_{0} = 6.0 × 10^{14} Hz.

What is the work function Φ of the material?

(a) Φ = -6.0 eV (b) Φ = -4.0 eV (c) Φ = +2.4 eV (d) Φ = +4.0 eV (e) Φ = +6.0 eV

(a) h = 6.0 × 10^{-34}J^{.}s (b) h = 6.2 × 10^{-34}J^{.}s (c) h = 6.4 × 10^{-34}J^{.}s (d) h = 6.6 × 10^{-34}J^{.}s (e) h = 6.8 × 10^{-34}J^{.}s