Download Physics 107 Exam #3 October 13, 1994 Your name: Multiple Choice

Physics 107
Exam #3
October 13, 1994
Your name:
Useful constants (multiple choice problems use the values given here):
neutron mass=1.675x10-27 kg electron mass=9.11x10-31 kg
c=3x108 m/s
1 eV=1.60x10-19 J
R=1.097x107 m-1
0=8.85x10-12 C2/Nm2
-27
-34
-15
proton mass=1.672x10 kg h=6.63x10 Js=4.14x10 eVs
=h/2
k=1.38x10-23 J/K=8.62x10-5 eV/K
You may come down to the front of the room and look at the periodic table.
Multiple Choice. 9 questions, 4 points each, 36 points total.
1. In the Maxwell-Boltzmann velocity distribution, the most probable molecular speed, vp, is (a)
greater than the average speed, v, (b) equal to the square root of 3kT/m, (c) less than the average
speed, v, (d) the same for all ideal gas molecules.
2. The expectation value of r for an electron in a hydrogen atom is (a)
1
∞
∞
∞
r
(a) ∫ 0 R* rR r 2 dr, (b) ∫ 0 R* rRdr, (c) ∫ 0 R* R r 2 dr, (d) ∫ r12 R* rR r 2 dr.
r
3. Molecules of a dilute gas which are identical, distinguishable particles obey
statistics. (a) Maxwell-Boltzmann, (b) Bose-Einstein, (c) Fermi-Dirac, (d) Rayleigh-Jeans.
4. We cannot think of the electron as orbiting the nucleus in any conventional sense because (a) the
Pauli exclusion principle prevents us from exactly specifying the electron's position, (b) the radial
part of the electron's wave function is independent of the orbital angle, (c) the Heisenberg
uncertainty principle prevents us from specifying the electron's position with arbitrary precision, (d)
the probability density * is independent of time and may vary considerably from place to place.
5. The wave function for two or more electrons occupying the same space must be antisymmetric
under particle exchange. This is another way to state the (a) Schrdinger equation, (b) conservation
of energy, (c) Heisenberg uncertainty principle, (d) Pauli exclusion principle.
6. An isolated H3 molecule, if it existed, would have more energy than a an isolated H2 molecule
plus an isolated H atom because (a) one of its three 1s electrons would have to be promoted to a
higher energy state to satisfy the Pauli exclusion principle, (b) its three 1s electrons would have
smaller uncertainties in their positions, (c) its three 1s electrons would have to have parallel spins,
(d) there are only two possible angular momentum states (+ and -) in a molecule.
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7. The orbital quantum numbers of the initial and final electron states for a transition in which a
single photon is emitted must differ by (a) zero, (b) 2l+1, (c) 1, (d) 2.
8. The electron's spin (a) results from the angular momentum of a spinning charged sphere, (b) can
take on any value between - and , (c) results from its intrinsic angular momentum, (d) gives rise
to a spin angular momentum of S= for the electron.
9. The Rayleigh-Jeans formula incorrectly predicts the energy density for a blackbody cavity
because (a) Bose-Einstein statistics do not apply to photons in a cavity, (b) it is not really
appropriate to think of photons in a cavity as originating from oscillators in the cavity wall, (c)
electrons are Fermions rather than Bosons, (d) electromagnetic waves in a cavity originate in
quantum mechanical rather than classical oscillators in the cavity walls.
Multiple Choice Short Problems. 7 problems, 8 points each, 56 points total.
1. The energy of the K x-rays of iron is (a) 6.38 keV, (b) 6.90 keV, (c) 30.9 keV, (d) 32.0 keV.
2. The most probable speed of an oxygen molecule (mass=5.32x10-26 kg) at room temperature (23
C) is (a) 115200 m/s, (b) 480 m/s, (c) 440 m/s, (d) 392 m/s.
3. The figure to the right shows the
electron, proton repulsion, and total
energies in H2+ as a function of proton
separation R for both symmetric and
antisymmetric states. By how much
(according to this figure) is the energy
of H2+ reduced compared to the total
energy of an isolated proton and
isolated hydrogen atom at infinite
separation R? (a) 2.7 eV, (b) 6.4 eV,
(c) 13.6 eV, (d) 16.3 eV.
4. An electron in hydrogen has a
principal quantum number of 3. The
maximum value of the electron's
orbital angular momentum is (a) 0 Js,
(b) 1.49x10-34 Js, (c) 2.59x10-34 Js,
(d) 3.66x10-34 Js.
5. There are
possible values of
ml for an atomic electron with l=4. (a)
7, (b) 8, (c) 9, (d) 14.
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6. The temperature of the sun's surface is 5800 K. What is the ratio of hydrogen atoms in the n=3
state compared to the n=1 state? (a) 5.52x10-9, (b) 2.84x10-10, (c) 9.46x10-11, (d) 5.93x10-12.
7. What is the wavelength of the most intense radiation from boiling water, temperature = 100C?
(a) 0.003 nm, (b) 7780 nm, (c) 9460 nm, (d) 12900 nm.
Problems. Two problems, 30 points total. Show all of your work on
separate pages. Answers without work shown receive no credit.
1. Electron probability density.
(a) (3 points) What is the radial wave function for a 1s electron in hydrogen.
(b) (2 points) What is the probability P(r)dr of finding this 1s electron somewhere between r
and r+dr from the nucleus?
(c) (10 points) Use calculus to find the most probable value of r for this 1s electron.
2. Molecular energies in an ideal gas. A nuclear reactor operates with its core in a pool of water
maintained at a constant temperature of 40 C. Neutrons produced in the reactor core come into
thermal equilibrium with the water before they escape from the pool. It is valid in this case to treat
the neutrons as ideal gas molecules subject to Maxwell-Boltzman statistics.
(a) (4 points) Calculate the average velocity of the neutrons in the reactor pool.
(b) (4 points) Calculate the most probable velocity of the neutrons in the reactor pool.
(c) (7 points) Calculate the most probable wavelength of the neutrons in the reactor pool.
Hints: the neutron mass is 1.675x10-27 kg. You need to use an important equation from an
earlier chapter. I will give it to you at a cost of 3 points if you forgot it.
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