Elements of Modern Physics
40
3. The energy required for ejecting the electrons may also be provided by
heating the metal, which results in the thermionic emission of the
electrons. They allows us to calculate, from quantum statistical mechanics,
the work function eφ. The value obtained agrees with the one obtained
from the photoelectric effect.
4. So far, it has been assumed that an electron receives energy only from a
single photon, the process being called a single-photon process. The
development of lasers has provided light beams of very high intensity
which allow us to observe multi-photon processes, in particular the multiphoton photoelectric effect. In this process, an electron ejected from a
metal receives energy from N photons. Its kinetic energy is given by
2
1
2
m
mv
Nhv e
=
− φ
(2.27)
and the critical frequency is eφ/Nh which is smaller than the corresponding
frequency for single-photon processes by a factor of 1/N.
In the analysis of the photoelectric effect, a photon was regarded as a
wave packet of energy, with no statements made for the quantization of
momentum. In fact since a significant amount of momentum was carried away
by the metal, conservation of momentum could not be usefully applied to the
photon-electron system. For the photon to acquire the bonafides of a particle, it
should have both a quantum of energy as well as a quantum of momentum. This
was demonstrated by the discovery of Compton effect (1922) in the scattering
of x-rays by electrons.
2.3 COMPTON EFFECT
Compton effect is essentially a demonstration of the scattering of a photon by
an electron as a particle-particle scattering.
Compton was concerned with the scattering of x-rays of wavelength λ 0 by
a thin film of metal. He measured the wavelength distribution of the scattered
rays at different scattering angles and found that it had two major components
in wavelength. One had essentially the same wavelength as the incident radiation,
i.e. λ 0 , while the other had a slightly longer wavelength [Fig. 2.3 (a)], with the
separation between the two wavelengths given by λ–λ 0 = λ c (λ – cos θ). Here
λ c is a constant which is independent of λ 0 or the scattering angle and is called
the Compton wavelength of the electron. This increase in wavelength or the
decrease in frequency is very difficult to understand in terms of the wave
description of radiation. However, it can be explained quite accurately by
considering the process as a scattering of photons regarded as particles with
well-defined energy and momentum by the electrons in the metal.
40
3. The energy required for ejecting the electrons may also be provided by
heating the metal, which results in the thermionic emission of the
electrons. They allows us to calculate, from quantum statistical mechanics,
the work function eφ. The value obtained agrees with the one obtained
from the photoelectric effect.
4. So far, it has been assumed that an electron receives energy only from a
single photon, the process being called a single-photon process. The
development of lasers has provided light beams of very high intensity
which allow us to observe multi-photon processes, in particular the multiphoton photoelectric effect. In this process, an electron ejected from a
metal receives energy from N photons. Its kinetic energy is given by
2
1
2
m
mv
Nhv e
=
− φ
(2.27)
and the critical frequency is eφ/Nh which is smaller than the corresponding
frequency for single-photon processes by a factor of 1/N.
In the analysis of the photoelectric effect, a photon was regarded as a
wave packet of energy, with no statements made for the quantization of
momentum. In fact since a significant amount of momentum was carried away
by the metal, conservation of momentum could not be usefully applied to the
photon-electron system. For the photon to acquire the bonafides of a particle, it
should have both a quantum of energy as well as a quantum of momentum. This
was demonstrated by the discovery of Compton effect (1922) in the scattering
of x-rays by electrons.
2.3 COMPTON EFFECT
Compton effect is essentially a demonstration of the scattering of a photon by
an electron as a particle-particle scattering.
Compton was concerned with the scattering of x-rays of wavelength λ 0 by
a thin film of metal. He measured the wavelength distribution of the scattered
rays at different scattering angles and found that it had two major components
in wavelength. One had essentially the same wavelength as the incident radiation,
i.e. λ 0 , while the other had a slightly longer wavelength [Fig. 2.3 (a)], with the
separation between the two wavelengths given by λ–λ 0 = λ c (λ – cos θ). Here
λ c is a constant which is independent of λ 0 or the scattering angle and is called
the Compton wavelength of the electron. This increase in wavelength or the
decrease in frequency is very difficult to understand in terms of the wave
description of radiation. However, it can be explained quite accurately by
considering the process as a scattering of photons regarded as particles with
well-defined energy and momentum by the electrons in the metal.