Physics 2220 (Schroeder) Name
fall 2005
Problem Set 11
(due Friday, November 11)
1. A lamp radiates 40 watts of energy at an average wavelength of 590 nm. (a) What
is the average energy of a photon emitted by this lamp? (Please express your answer
both in joules and in electron-volts.) (b) Roughly how many photons does the lamp
emit in one second?
2. Consider the photoelectric effect experiment described in class, in which sodium metal
is illuminated with monochromatic light and the voltage that builds up between the
electrodes is measured with a high-resistance voltmeter (which allows essentially no
current to pass). When the wavelength of the light is 420 nm, the voltage reading
is 0.65 V; when the wavelength is 310 nm, the voltage reading is 1.69 V. From this
information, calculate Planck’s constant and the work function for sodium.
3. Does the data described in the previous problem disprove the wave model of light? If
so, why? If not, what additional information would be necessary?
4. When an electron and its antiparticle, a positron, annihilate each other, the reaction
produces two gamma-ray photons, each with an energy of 511,000 eV. (a) What is the
momentum of such a photon? (b) What is its wavelength? (c) What is its frequency?
5. A high-power pulsed laser emits a burst of light carrying a total energy of one joule.
This light hits a mirror and bounces straight back. (a) By how much does the mo-
mentum of the light change as it bounces off the mirror? (b) If the mass of the mirror
is one gram and it is free to move but initially at rest, what is its recoil velocity? (c)
If the wavelength of the light is 500 nm, how many photons are in the burst?
6. A bullet of mass 40 g travels at a speed of 1000 m/s. (a) What is its de Broglie
wavelength? (b) Why is the wave nature of the bullet not revealed by diffraction
effects, say, when it passes through a doorway?
7. In an ordinary television set, electrons are accelerated through a voltage difference of
25 kV. What is the de Broglie wavelength of these electrons?
8. Calculate the wavelength of each of the following particles, assuming that its kinetic
energy is 1.0 keV: (a) an electron; (b) a photon; (c) a neutron.
9. A modified oscilloscope is used to perform an electron interference experiment. Elec-
trons are incident on a pair of slits 0.060 µm apart. The bright bands in the interference
pattern are separated by 0.40 mm on the screen, 20 cm away from the slits. Find the
voltage difference that the electrons were accelerated through to give this pattern.
10. Imagine playing baseball in a universe (not ours!) where Planck’s constant is 0.60 J-s.
What would be the minimum uncertainty in the position of a 0.50 kg baseball traveling
at 20 m/s, if the uncertainty in its speed is 1 m/s?
11. Draw a wavefunction with a small ∆xand a large ∆px. Then draw a wavefunction
with a small ∆pxand a large ∆x. Finally, draw a wavefunction with a large ∆xand
a large ∆px. (Hint: To have a small ∆px, the wave must go through many cycles with
a well-defined wavelength.)
