Page 428 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 33] PHYSICAL AND QUANTUM OPTICS 413

QUANTUM THEORY OF LIGHT
Certain features of the behavior of light can be explained only on the basis that light consists of individual quanta,
or photons, which we can think of as tiny bundles of electromagnetic energy. The energy of a photon of light
whose frequency is f is

Quantum energy = E = hf

where h is Planck’s constant:

Planck’s constant = h = 6.63 × 10 −34 J·s

A photon has most of the properties associated with particles—it is localized in space and possesses energy and
momentum—but it has no mass. Photons travel with the velocity of light.
The electromagnetic and quantum theories of light complement each other: Under some circumstances light
exhibits a wave character, under other circumstances it exhibits a particle character. Both are aspects of the same
basic phenomenon.

SOLVED PROBLEM 33.7
What are some of the differences between photons and electrons?

Electrons have mass, photons do not. Electrons have electric charge, photons do not. Electrons may be stationary,
photons move only at the velocity of light. Electrons are constituents of ordinary matter, photons are not. The energy
of a photon depends only on its frequency, that of an electron depends on its velocity and position.

SOLVED PROBLEM 33.8
14
The human eye can respond to as few as three photons of light. If the light is yellow ( f = 5 × 10 Hz),
how much energy does this represent?
The energy of each photon is

14
E = hf = (6.63 × 10 −34 J·s)(5 × 10 Hz) = 3.3 × 10 −19 J
The total energy is 3E = 10 −18 J.

SOLVED PROBLEM 33.9
The average wavelength of the light emitted by a certain 100-W light bulb is 5.5 × 10 −7 m. How many
photons per second does the light bulb emit?
The frequency of the light is
8
c 3 × 10 m/s
14
f = = = 5.5 × 10 Hz
λ 5.5 × 10 −7 m
and the energy of each photon is
14
E = hf = (6.63 × 10 −34 J·s)(5.5 × 10 Hz) = 3.6 × 10 −19 J
Since 100 W = 100 J/s, the number of photons emitted per second is

100 J/s
20
= 2.8 × 10 photons/s
3.6 × 10 −19 J/photon