NAME______
PHYSICS 39
Practice Final Exam (Chapters 38-42, 44 - 46)
Note: These are not the only types of problems that may occur on the final exam.
1. Joe and Sally are twins who are 5.0 years old, when one of them takes a round-trip journey on a space ship and travels for a total of 40.0 years. When they finally meet again, Sally is 45.0 years old, and Joe is 5.5 years old. (a) Which one of them went on the trip? (b) What was the average speed of the space ship, in terms of c? (Keep 5 sig. figs.)
a. Joe
b. 0.99992 c
2. The expansion of the Universe causes the light from the most distant galaxies to be red-shifted into the infra-red. Suppose a galaxy whose peak wavelength is 500 nm is moving away from us at 98% of the speed of light. What peak wavelength would we be seeing here on Earth?
= 4.98 m
3. A 0.001 60-nm photon (1.60 X 10-12 m) is moving in a direction 35.0 ccw from the +x axis. It Compton-scatters from a free electron with the result that its wavelength is increased to a final value of 0.00220 nm by the collision. What will be direction of the scattered photon (with respect to the x axis)?
76.1
4. Suppose that 460-nm light strikes a metal, resulting in ejected electrons having a maximum kinetic energy of 1.70 eV. What would be the work function of the metal (in eV)?
= 1.00 eV
5. An electron has a kinetic energy of 12.0 eV. The electron is incident upon a rectangular barrier of height 20.0 eV and width 0.100 nm. Find the probability that the electron will tunnel through the barrier.
0.055
6. The wave function for a particle is given by (x) =Ax, where A is a constant, A = 10.0. Find the probability that the particle will be found between x = 0.300 and x = 0.400.
1.23
7 An electron in a sodium atom is in the O shell (n = 5). Determine the maximum value of Lz.
4h/2
8. (a) Write out the electronic configuration of the ground state for boron (five protons). (b) Write out the values for the possible set of quantum numbers n, l, ml, and ms for the electrons in boron. (c) Calculate the orbital angular momentum of the electron with the highest value of l in part (b) in terms of h/2.
a. 1s22s2p1
c. (2)h/2
9. Find the ionization energy (in eV) for doubly ionized Lithium Li++ in the fourth excited state. Lithium has three protons in its nucleus.
.
-4.90 eV
10. A sample of radioactive material contains 1.00 X 1015 atoms and has an activity of 6.00 X 1011 Becquerels. How many atoms will remain undecayed after one hour?
1.15 X 1014
11. Suppose two kilograms of hamburger receives 46 Joules of energy by being irradiated with alpha particles. Calculate the minimum dose received by the hamburger in rems.
23000 – 46000 rems
12. The quark composition of the o particle is uds. Show that the charge, baryon number and strangeness of this particle equals the sums of these numbers for the quark constituents.
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Possibly Useful Formulas:
Single Slit:
sin dark = /alimiting angle of resolution: min = /a
Circular aperture:
limiting angle of resolution: min = 1.22 /D ( in radians)
Diffraction Grating:
d sin bright = m m = 0, 1, 2, 3 …. Bragg’s Law
X-ray crystal diffraction:
2d sin = m (constructive interference) m = 1, 2, 3, ...
Polarizing filter: I = Imax cos2 Malus’ Law
Complete polarization by reflection: tan p = n2/n1 Brewster’s Law
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h = 6.626 X 10-34 J-s
mass of electron me = 9.109 X 10-31 kg
Compton Effect:
= - o = __h_ (1 – cos )
mec
where h/mec = 0.002 43nm
De Broglie wavelength:
= h / p where p = momentum
Photoelectric effect:
KE = ½ mv2
KEmax = hf -
Ephoton = hf = hc/
c = f
Particle in a Box:
En = n2 n = 1, 2, 3, …
Probability of finding a particle between limits:
Pab = 2 dx
Normalization: 2 dx = 1
Expectation value: x = dx
Tunneling probability:
Transmission coefficient, T = e-2CL where C =
Reflection coefficient R = 1 - T
Allowed energy states for a hydrogen-like atom:
En = -13.606 eV ( z2/n2 )
Orbital Angular Momentum:
L = h/2
Lz = mlh/2
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R = dN/dt = -N, = decay constant
Ro = -oN
N = N0 e-t R = R0 e-t where R = decay rate in decays/sec (Bq)
T½ = 0.693/
One rad is that amount of radiation that increases the energy of 1 kg of absorbing material by 0.01 Joule.
One rem is the product of the dose in rad and the RBE factor.
RadiationRBE Factor
X-rays and gamma rays1.0
Beta particles1.0 – 1.7
Alpha particles10 – 20
Thermal neutrons4.5
Heavy ions20
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