PHYSICS 252: TEST 3 4/13/15
Dr. Varriano
NAME:_______________________
Do all 8 problems. The point value for each problem is indicated next to the problem number. Show all of your work in the space
provided to receive partial credit. You may use additional sheets of paper if necessary. Be sure to turn in the additional sheets with
your name written on each sheet. Put your final answer to each question on the line provided unless instructed otherwise.
___________________________________________________________________
1. [12 pts]
(a) The peak wavelength of the light from the Sun is around 580 nm. Find the approximate temperature of the Sun’s surface.
5000 K
(b) The Sun emits approximately 4x1026 J of energy each second. Assuming that it’s a spherical blackbody (not a bad assumption),
find the diameter of the Sun. (Recall that the surface area of a sphere is 4 times the square of the radius.)
1.9 Gm
(c) On the axes provided, sketch the intensity vs. wavelength spectrum of the Sun’s thermal radiation. On the same axes, plot what
classical theory (Rayleigh-Jeans) predicts for the spectrum. Be sure to label the actual curve and the classically predicted curve to
distinguish the two.
Review!
Intensity
0
Wavelength
2.[14 pts]
A particular PMT has 8 dynodes. Each dynode has a secondary emission ratio of 3. The PMT will not detect light with a wavelength
longer than 870 nm.
(a) Explain how the photon model of light explains why this PMT does not work for wavelengths longer than 870 nm.
Review!
(b) What is the work function of the photocathode employed in the PMT?
1.429 eV
(c) Assuming that the photocathode is ideal, i.e. a quantum efficiency of unity, how much current would be produced at the PMT's
anode if 25 picoWatts of 500-nm light entered the PMT?
65.9 nA
2
3. [18 pts]
A Hydrogen atom is in the second excited state (n = 3). Using the Bohr model, answer the following.
(a) How far is the electron from the proton?
4.77 Å
(b) Find the shortest wavelength of light that can be emitted by this atom in the n=3 state.
102.8 nm
(c) Find the longest wavelength of light that can be absorbed by this atom in the n=3 state.
1883 nm
(d) Can this atom in the n=3 state emit an infrared photon? Circle either “yes” or “no” and then explain your answer.
Yes
No
4.[10 pts]
A photon emitted by a laser pointer has 2.29 eV of energy. How fast must an electron travel so that its matter wavelength is equal to
the wavelength of this photon?
1341 m/s
5.[10 pts]
Consider an electron confined in one dimension (the x-axis) in a certain layer of material that is 75 Å wide. The potential energy
function of the electron can be approximated by a one-dimensional infinite square well where the width of the layer is the width of the
well. The ground-state eigenfunction of this electron is given by   A sin( π x / 75) where x is in Angstroms.
(a) Write down the one-dimensional time-independent Schrödinger equation.
Review!
(b) How long is the wavelength of the electron in the ground state?
150 Å
(c) Which one of the following four expressions would give you the probability of finding the electron in the middle third of the layer?
(Circle the one correct expression.)

50
50

25
25
2
2
 A sin ( π x / 75)dx
2
2
 A sin ( π x / 75)dx
 A sin( π x / 75)dx
A2
(d) If the width of the confining layer is decreased, what happens to the ground state energy of the electron? (Circle the correct
choice.)
increases / decreases / remains the same
3
6. [16 pts]
An Argon ion laser can be tuned to lase at a couple of different visible wavelengths. One is green and another is blue with a
wavelength of 488 nm. Suppose the laser is tuned to the blue wavelength and is emitting 4 W of power.
(a) How much energy does each blue photon carry in the output beam? (Answer in electronVolts.)
2.55 eV
(b) Find the number of photons leaving the laser each second.
9.8x1018
(c) The laser is now tuned to the green wavelength but it still delivers 4 W of output power. Complete the following statements by
filling in the blanks with either increases, decreases, or doesn’t change. A word choice can be used more than once.
"The energy of a photon
decreases
and the photon rate increases
.“
(d) The power emitted at the green wavelength is now decreased. Which of the following has occurred? (Circle the number before the
one correct choice.)
1.
2.
3.
The energy of a photon has decreased.
The number of photons leaving the laser each second has decreased
The product of the photon energy and photon rate has decreased.
7. [10 pts]
(a) Which of the following will increase the maximum energy of an emitted x-ray photon in an x-ray tube? (Circle the number before
the correct choice(s). There may be more than one correct choice.)
1.
2.
3.
increase the electron's accelerating voltage
increase the density of the target material
increase the number of electrons hitting the target
(b) An accelerating voltage of 12.43 kV is used in an x-ray tube. What is the shortest wavelength of x-ray that this tube can produce?
0.1 nm = 1 Å
(c) Does classical wave theory or quantum (photon) theory explain the emission of the characteristic x-rays from a target?
quantum
8. [10 pts]
(a) Which one phrase best describes “Compton scattering”? (Circle the number before the best choice.)
1.
2.
3.
the ejection and scattering of electrons from a metal that has been hit with light
the scattering of visible light off of air molecules in the atmosphere
the scattering of x-ray light off of electrons
(b) Which model of light is used to explain the results of Compton scattering? (Circle one choice.)
wave model
(c) Briefly explain why the Compton scattered light always has a longer wavelength than the incident light.
Some of the energy of the incident x-ray goes to kinetic energy of the
ejected electron so the scattered x-ray has less energy than the incident
x-ray. Less energy means longer wavelength.
photon model