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
(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
If we measure the particle's position in the well, which is the more
(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 E1, keeping E2 constant.
(b) Increase |E2 - E1|.
(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) = aΨ1 +
bΨ3 , where Ψ1 and
Ψ3 are individually normalized.
What is the frequency of oscillation f of the spatial
(a) f = 1.27 × 1014 Hz
(b) f = 2.54 × 1014 Hz
(c) f = 3.24 × 1014 Hz
(d) f = 3.55 × 1015 Hz
(e) f = 2.29 × 1015 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) P3 = 1.00
(b) P3 = 0.399
(c) P3 = 0.518
(d) P3 = 0.841
(e) P3 = 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
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
(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
(e) all 10
(a) <KE> = <KE0>
(b) <KE> = 2 <KE0>
(c) <KE> = 4 <KE0>
(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 vbrain = 1540 m/s, or propagates around the periphery through the skull bone (assumed to be spherical for this problem) at vskull = 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/m2. 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/m2. What is the net intensity I at your right
(a) I = 0 W/m2
(b) I = 0.8 W/m2
(c) I = 1.5 W/m2
(d) I = 6.2 W/m2
(e) I = 7.0 W/m2
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) θmin = 1°
(b) θmin = 2°
(c) θmin = 4°
(d) θmin = 8°
(e) θmin = 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 ao,Li the most likely distance for the
electron in a Li++ atom to be from the nucleus, with
ao,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) ao,Li < ao,H
(b) ao,Li = ao,H
(c) ao,Li > ao,H
(a) λmax = 0.665 nm
(b) λmax = 10.1 nm
(c) λmax = 21 nm
(d) λmax = 137 nm
(e) λmax = 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
(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) Equantum dot / Emolecule = 1
(b) Equantum dot / Emolecule = 6/5
(c) Equantum dot / Emolecule = 5/3
(d) Equantum dot / Emolecule = 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,
E1 = -1.5 eV and E2 = +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.
Ψ1(x) is the wave function of the ground
state, and Ψ2(x) is the wave function of
the first excited state.
Which one of the following statements is not true?
(a) Ψ1(A) = Ψ1(F)
(b) Ψ2(A) = -Ψ2(F)
(c) Both Ψ1 and Ψ2 are proportional to sin(kx) in the regions A < x < B and D < x < F (though 'k' might be different for Ψ1 and Ψ2)
(d) dΨ1/dx = 0 at x = C
(e) d|Ψ2|2/dx > 0 for x < A
(c) They are the same.
(a) f = 4.8 × 1014 Hz
(b) f = 3.6 × 1014 Hz
(c) f = 1.24 × 1014 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
f0 = 6.0 × 1014 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 × 10-34J.s
(b) h = 6.2 × 10-34J.s
(c) h = 6.4 × 10-34J.s
(d) h = 6.6 × 10-34J.s
(e) h = 6.8 × 10-34J.s