of photons emitted by the transmitter per second, as in example 7,
but that even by the time they spread out and reach the receiving
antenna, there should be many photons overlapping each other
within a space of one cubic wavelength. Problem 47 on p. 950
verifies that the number is in fact extremely large.
Momentum of a photon example 9
.According to the theory of relativity, the momentum of a beam
of light is given byp =E/c. Apply this to find the momentum
of a single photon in terms of its frequency, and in terms of its
wavelength.
.Combining the equationsp=E/candE=hf, we findp=E/c=h
c
f.To reexpress this in terms of wavelength, we usec=fλ:p=
h
c·
c
λ
=
h
λThe second form turns out to be simpler.Discussion Questions
A The photoelectric effect only ever ejects a very tiny percentage of
the electrons available near the surface of an object. How well does this
agree with the wave model of light, and how well with the particle model?
Consider the two different distance scales involved: the wavelength of the
light, and the size of an atom, which is on the order of 10−^10 or 10−^9 m.
B What is the significance of the fact that Planck’s constant is numeri-
cally very small? How would our everyday experience of light be different
if it was not so small?
C How would the experiments described above be affected if a single
electron was likely to get hit by more than one photon?
D Draw some representative trajectories of electrons for∆V= 0,∆V
less than the maximum value, and∆Vgreater than the maximum value.
E Explain based on the photon theory of light why ultraviolet light would
be more likely than visible or infrared light to cause cancer by damaging
DNA molecules. How does this relate to discussion question C?
F DoesE=hfimply that a photon changes its energy when it passes
from one transparent material into another substance with a different in-
dex of refraction?
Section 13.2 Light as a particle 877