14.4 The Old Quantum Theory
645
2πhc 2
k B T
hc
4 π 4
15
2π 5 k 4
15h 3 c 2 T 4 σT 4
σ
2π 5 (1.3807 × 10 −23 J K −1 ) 4
15(6.6261 × 10 −34 J s) 3 (2.9979 × 10 8 m s −1 ) 2
5.671 × 10 −8 J m −2 s −1 K −4
This value agrees well with the experimental value, 5.669 × 10 −8 J m −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 as λ → ∞, 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 a threshold wavelength that depends on the identity
of the metal. This phenomenon is known as the photoelectric 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
E hν
hc
λ
(14.4-8)
where h is Planck’s constant, ν is the frequency of the radiation, λ is its wavelength,
and c is the speed of light. Equation (14.4-8) is known as the Planck–Einstein relation.
The quanta of light are called photons.
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. The work function
W is the minimum energy required to detach an electron from a given substance. The
maximum electron kinetic energy is
E max hν − W
hc
λ
− W
(14.4-9)
In 1916, RobertA. 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).
645
2πhc 2
k B T
hc
4 π 4
15
2π 5 k 4
15h 3 c 2 T 4 σT 4
σ
2π 5 (1.3807 × 10 −23 J K −1 ) 4
15(6.6261 × 10 −34 J s) 3 (2.9979 × 10 8 m s −1 ) 2
5.671 × 10 −8 J m −2 s −1 K −4
This value agrees well with the experimental value, 5.669 × 10 −8 J m −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 as λ → ∞, 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 a threshold wavelength that depends on the identity
of the metal. This phenomenon is known as the photoelectric 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
E hν
hc
λ
(14.4-8)
where h is Planck’s constant, ν is the frequency of the radiation, λ is its wavelength,
and c is the speed of light. Equation (14.4-8) is known as the Planck–Einstein relation.
The quanta of light are called photons.
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. The work function
W is the minimum energy required to detach an electron from a given substance. The
maximum electron kinetic energy is
E max hν − W
hc
λ
− W
(14.4-9)
In 1916, RobertA. 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).