April 23, 1999 Physics 208
Print your name and section clearly on all five pages. (If you do not
know your section number, write your TA’s name.) Show all work in the space
immediately below each problem. Your final answer must be placed in the
box provided. Problems will be graded on reasoning and intermediate steps
as well as on the final answer. Be sure to include units wherever necessary,
and the direction of vectors. Each problem is worth 25 points. In doing
the problems, try to be neat. Check your answers to see that they have
the correct dimensions (units) and are the right order of magnitudes. You
are allowed one 8½ x 11" sheet of notes and no other references.
The exam lasts exactly 50 minutes.
(Do not write below)
Problem 1: __________
Problem 2: __________
Problem 3: __________
Problem 4: __________
1. A laser beam is incident on a pair of slits separated by 0.12 mm.
a. What is the slit-to-screen distance if the bright fringes are 5.0 mm apart and the laser light has a wavelength of 633 nm? (9 pts.)
b. What will be the fringe spacing on the screen above with 480-nm light? (8 pts.)
c. If the whole apparatus is immersed in water with an index of refraction of 1.33, what will be the fringe spacing on the screen for the 480-nm light above? (8 pts.)
2. An advanced civilization has developed a 1000-kg spaceship that goes, with respect to the galaxy, only 50 km/s slower than light.
b. What is the galactic diameter as measured in the ship’s frame of
reference? (6 pts.)
c. What is the momentum of the spaceship in the frame of reference of
the galaxy? (6 pts.)
d. What work must be done on the spaceship to accelerate it to this
speed from rest? (6 pts.)
3. A hydrogen discharge emits light with a wavelength of 103 nm.
a. What principal quantum numbers are involved in this transition? (7 pts.)
b. What is the energy of the emitted photons (in eV)? (6 pts.)
c. If these photons are incident on a metal with a work function of 4.1 eV, what is the maximum energy of the ejected electrons? (6 pts.)
d. What is the minimum de Broglie wavelength of the electrons ejected above (6 pts.)
4. A neutral copper atom contains 29 electrons.
a. How many electrons are in the L shell in the ground state of copper? (5 pts.)
b. What is the orbital angular momentum of an electron in the 2p state? (5 pts.)
c. What is the energy (in eV) of the Ka characteristic x-ray emitted by copper? (5 pts.)
d. What is the wavelength of the x-ray calculated above? (5 pts.)
e. To what quantum state would you expect the outermost (valence) electron of copper in the 4s state to be excited by the absorption of a photon of the lowest possible energy? (5 pts.)