For some of these homework problems, you may find it convenient
to refer to the diagram of the electromagnetic spectrum shown in
section 6.4 of Electricity and Magnetism.
Give a numerical comparison of the number of photons per
second emitted by a hundred-watt FM radio transmitter and a
Two different flashes of light each have the same energy. One
consists of photons with a wavelength of 600 nm, the other 400 nm.
If the number of photons in the 600-nm flash is 3.0×1018, how many
photons are in the 400-nm flash?
When light is reflected from a mirror, perhaps only 80% of the
energy comes back. The rest is converted to heat. One could try
to explain this in two different ways: (1) 80% of the photons are
reflected, or (2) all the photons are reflected, but each loses 20% of
its energy. Based on your everyday knowledge about mirrors, how
can you tell which interpretation is correct?
[Based on a problem
from PSSC Physics.]
Suppose we want to build an electronic light sensor using an
apparatus like the one described in the section on the photoelectric
effect. How would its ability to detect different parts of the spectrum
depend on the type of metal used in the capacitor plates?
The photoelectric effect can occur not just for metal cathodes
but for any substance, including living tissue. Ionization of DNA
molecules can cause cancer or birth defects. If the energy required to
ionize DNA is on the same order of magnitude as the energy required
to produce the photoelectric effect in a metal, which of these types
of electromagnetic waves might pose such a hazard? Explain.
60 Hz waves from power lines
100 MHz FM radio
microwaves from a microwave oven
ultra violet light
The beam of a 100-W overhead projector covers an area of
1 m × 1 m when it hits the screen 3 m away. Estimate the number
of photons that are in flight at any given time. (Since this is only
an estimate, we can ignore the fact that the beam is not parallel.)
The two diffraction patterns were made by sending a flash of
light through the same double slit. Give a numerical comparison of
the amounts of energy in the two flashes.
Three of the four graphs are properly normalized to represent
single photons. Which one isn't? Explain.
Photon Fred has a greater energy than photon Ginger. For
each of the following quantities, explain whether Fred's value of
that quantity is greater than Ginger's, less than Ginger's, or equal
to Ginger's. If there is no way to tell, explain why.
electric field strength
magnetic field strength
Give experimental evidence to disprove the following interpretation
of wave-particle duality: A photon is really a particle, but
it travels along a wavy path, like a zigzag with rounded corners. Cite
a specific, real experiment.
In the photoelectric effect, electrons are observed with virtually
no time delay (∼ 10 ns), even when the light source is very weak.
(A weak light source does however only produce a small number of
ejected electrons.) The purpose of this problem is to show that the
lack of a significant time delay contradicted the classical wave theory
of light, so throughout this problem you should put yourself in
the shoes of a classical physicist and pretend you don't know about
photons at all. At that time, it was thought that the electron might
have a radius on the order of 10-15 m. (Recent experiments have
shown that if the electron has any finite size at all, it is far smaller.)
(a) Estimate the power that would be soaked up by a single electron
in a beam of light with an intensity of 1 mW/m2.
(b) The energy, W, required for the electron to escape through the
surface of the cathode is on the order of 10-19 J. Find how long it
would take the electron to absorb this amount of energy, and explain
why your result constitutes strong evidence that there is something
wrong with the classical theory.