Elements of Modern Physics
32
In this chapter, the background which necessitated the introduction of quantum
theory of matter and radiation is discussed. We describe Planck’s theory of
black-body radiation, photoelectric effect, Compton scattering, matter waves
and Davisson-Germer experiment, Rutherford scattering, and the Bohr theory
of an atom. The choice of these topics is dictated by their historical importance
and the directness with which they lead to the basic rules of quantum mechanics.
Though most of these primitive quantum ideas have been replaced by the more
universal description in terms of wave mechanics, they still serve a useful purpose
in providing a simple picture of quantum phenomena.
Quantum mechanical effects become important in the domain of small
distances. To be more precise, the effects are important in measurements which
require the knowledge of, say, the momentum p x and position x of a system to an
accuracy such that
(∆ p x ) (∆ x) ~ h
(2.1)
where ∆ p x and ∆ x are the errors in the measurement of the x-component of
momentum and position of the system, and h is a small number whose value in
mks unit is
h = 6.67 × 10
–34
Js
(2.2)
It is worth pointing out that once again radiation plays an important role in
the development of quantum mechanics, through for a different reason: the
ideas of wave functions and wave equations already existed for radiation; they
only required a reinterpretation in terms of the photon which is the quantum of
radiation.
2.1 BLACK-BODY RADIATION
Historically, the first indication of the inadequacy of classical ideas to explain
the properties of matter, occurred in what is termed as black-body radiation.
A black-body is a body which absorbs all the radiation incident on it, and hence
is the perfect absorber. Consideration of equilibrium of different bodies at the
same temperature implies that it is also the best emitter of radiation energy. A
black-body may be idealized by a small hole drilled in a cavity.
If the radiation from a black-body is analysed by a spectrometer
(i.e. a prism of a grating), it is found (Lummer and Pringsheim, 1900) that the
intensity distribution as a function of wavelength, has a well-defined shape
(Fig. 2.1). What is most significant is that, for a given temperature, it is a universal
curve independent of the properties of the walls of the cavity. In particular, it
has a maximum at some wavelength λ m . As the temperature of the black-body
is raised, the intensity of radiation increases at each wavelength, and λ m shifts to
a smaller value such that
32
In this chapter, the background which necessitated the introduction of quantum
theory of matter and radiation is discussed. We describe Planck’s theory of
black-body radiation, photoelectric effect, Compton scattering, matter waves
and Davisson-Germer experiment, Rutherford scattering, and the Bohr theory
of an atom. The choice of these topics is dictated by their historical importance
and the directness with which they lead to the basic rules of quantum mechanics.
Though most of these primitive quantum ideas have been replaced by the more
universal description in terms of wave mechanics, they still serve a useful purpose
in providing a simple picture of quantum phenomena.
Quantum mechanical effects become important in the domain of small
distances. To be more precise, the effects are important in measurements which
require the knowledge of, say, the momentum p x and position x of a system to an
accuracy such that
(∆ p x ) (∆ x) ~ h
(2.1)
where ∆ p x and ∆ x are the errors in the measurement of the x-component of
momentum and position of the system, and h is a small number whose value in
mks unit is
h = 6.67 × 10
–34
Js
(2.2)
It is worth pointing out that once again radiation plays an important role in
the development of quantum mechanics, through for a different reason: the
ideas of wave functions and wave equations already existed for radiation; they
only required a reinterpretation in terms of the photon which is the quantum of
radiation.
2.1 BLACK-BODY RADIATION
Historically, the first indication of the inadequacy of classical ideas to explain
the properties of matter, occurred in what is termed as black-body radiation.
A black-body is a body which absorbs all the radiation incident on it, and hence
is the perfect absorber. Consideration of equilibrium of different bodies at the
same temperature implies that it is also the best emitter of radiation energy. A
black-body may be idealized by a small hole drilled in a cavity.
If the radiation from a black-body is analysed by a spectrometer
(i.e. a prism of a grating), it is found (Lummer and Pringsheim, 1900) that the
intensity distribution as a function of wavelength, has a well-defined shape
(Fig. 2.1). What is most significant is that, for a given temperature, it is a universal
curve independent of the properties of the walls of the cavity. In particular, it
has a maximum at some wavelength λ m . As the temperature of the black-body
is raised, the intensity of radiation increases at each wavelength, and λ m shifts to
a smaller value such that