Physical Chemistry Third Edition

14.4 The Old Quantum Theory 645

 2 πhc^2

(

kBT

hc

) 4

π^4

15



2 π^5 k^4

15 h^3 c^2

T^4 σT^4

σ

2 π^5 (1. 3807 × 10 −^23 JK−^1 )^4

15(6. 6261 × 10 −^34 Js)^3 (2. 9979 × 108 ms−^1 )^2

 5. 671 × 10 −^8 Jm−^2 s−^1 K−^4

This value agrees well with the experimental value, 5.669× 10 −^8 Jm−^2 s−^1 K−^4.

Exercise 14.13

Find the temperature that corresponds to the wavelength of maximum spectral emittance at

650.0 nm, in the red part of the visible spectrum.

Exercise 14.14

Show that in the limit asλ→∞, Eq. (14.4-5) agrees with Eq. (14.4-2).

Einstein’s Theory of the Photoelectric Effect

When a metal plate in a vacuum is illuminated, it emits electrons if the wavelength of the

incident light is at least as small as athreshold wavelengththat depends on the identity

of the metal. This phenomenon is known as thephotoelectric effect. Early investigators

were surprised to find that the maximum energy of the ejected electrons depended only

on the wavelength of the light and not on its intensity. There was no explanation for

this behavior until 1905, when Einstein published his theory of the photoelectric effect,

which we regard as the second theory of the “old quantum theory.” This theory is based

on the hypothesis that the energy in a beam of light consists of discrete “quanta,” and

that each quantum has an energy

Ehν

hc

λ

(14.4-8)

wherehis Planck’s constant,νis the frequency of the radiation,λis its wavelength,

andcis the speed of light. Equation (14.4-8) is known as thePlanck–Einstein relation.

The quanta of light are calledphotons.

Albert Einstein, 1879–1955, was a
German-Swiss-American physicist who
received the 1921 Nobel Prize in
physics for this work. He was the
greatest physicist of the 20th century
and made fundamental contributions in
many areas of theoretical physics.

The name “photon” was coined by the
American chemist G. N. Lewis,
1875–1946, who became famous for his
invention of the “octet rule” of chemical
bonding and his careful statement of
the third law of thermodynamics.

The energy of an electron ejected from the metal is equal to the energy of the photon

minus the energy required to detach the electron from the metal. Thework function

Wis the minimum energy required to detach an electron from a given substance. The

maximum electron kinetic energy is

Emaxhν−W

hc

λ

−W (14.4-9)

In 1916, Robert A. Millikan (the same person who measured the electron’s charge) made

accurate measurements of the photoelectric effect that agreed well with Eq. (14.4-9).