Physics 3101, Introduction to Modern Physics, Spring 2005
EXAM #1
Friday, February 11, 2005
Instructions
Read each problem carefully before starting. Choose 3 of the following 4 problems.
Remember to work each problem as fully as possible. Partial credit will be given so
SHOW ALL OF YOUR WORK!!
Constants:
c = 3 x 108 m/s
h = 6.63 x 10-34 J s = 4.14 x 10-15 eV s
1
k=
= 8.99 x 109 N m2/C2
hc = 1240 eV nm
4πε 0
k = Boltzmann’s constant = 1.38 x 10-23 J/K = 8.61 x 10-5 eV/K
h = h/2π
me = 9.11 x 10-31 kg
1 MeV/c2 = 1.783 x 10-30 kg
1. A person gets in a spaceship and makes a roundtrip journey to the star Sirius A, located
8.6 light years away. According to the person, the total time elapsed during the entire
voyage is 4 years.
(a) How fast was the spaceship traveling? Assume constant velocity for the entire
journey. Hint: Analyze the problem using length contractions from the point of
view of the spaceship.(13 points)
(b) How much time has elapsed on earth during the time the spaceship was away? (10
points)
(c) If the spaceship is 1000 m long in its rest frame, how long is the spaceship during
the voyage as measured from earth? (10 points)
2. A neutral ‘K’ particle (rest mass mK) at rest spontaneuously decays into a ‘W’ particle
(rest mass mW) and a γ-ray photon (mass = 0) as shown in the figure. After the decay, the
W particle and the travel in opposite directions.
Before:
mK
After:
mW
γ
(a) What are the total energy and momentum of the ‘K’ particle before it decays? (8
points)
(b)
What is the total momentum of the W particle mK, mW and c? (12 points)
(c) What is the total momentum of the γ-ray photon mK, mW and c? (8 points)
(d) Which particle has the heavier rest mass, the K or the W particle? (5 points)
3. (a) The work function of silver (Ag) is 4.73 eV. Compute the threshold wavelength
(in nm) for the photoelectric effect. If 5 W of light at that wavelength impinges
on the surface of silver, how many electrons are emitted per second? (17 points)
(b) Assuming the earth is an ideal blackbody, compute the equilibrium surface
temperature of the earth (in K) if the solar energy reaching the earth is 1.36 x 103
W/m2. Does your answer make sense? (16 points)
4. Sulfur has an atomic number of Z = 16. It is possible to create S15+, i.e., a sulfur ion
that has one bound electron. Using the Bohr model, answer the following questions:
(a) Compute the ground state energy of S15+. (12 points)
(b) Write down the angular momentum of the n=1,2,3 states of S15+. (8 points)
(c) Compute the frequency of the orbit of the n=29 state. (13 points)