Elements of Modern Physics
66
ln Chapter 2, we have discussed some experiments which indicate that radiation
should be regarded as being made up of zero-mass particles called photons
each of which carries a quantum of energy hv and momentum
h
c
v n . It was
also observed that particles with nonzero mass, such as the electron, have wave
properties associated with them, and produce diffraction patterns similar to those
produced by radiation. Thus, a situation emerges in which radiation and matter
exhibit both particles properties, i.e., they carry quantum of energy and
momentum, and wave properties, i.e., they produce diffraction patterns.
Here, the basic laws governing the wave-particle behaviour of matter will
be analysed and applied to some simple cases. In deducing the laws, we will
borrow heavily from the wave properties of radiation and particle properties of
matter particles, with which one is familiar.
3.1 A THOUGHT EXPERIMENT
Consider a thought experiment in which a beam of particles is incident on two
closely-spaced narrow slits S 1 and S 2 , as shown in Fig. 3.1 These slits act as
two coherent sources and produce interference fringes on a screen S placed at
a distance so far away that the separation between the slits is negligible compared
to their distance from the screen. This experiment is Young’s double slit experiment
for radiation, but here it is reanalysed in terms of the particle which constitute
the beam.
The intensity variation on the screen is given by the familiar interference
fringes. The interpretation of the interference fringes in terms of the particles is
that the intensity is proportional to the number of particles arriving at various
points, with no particles coming to regions with zero intensity. It is to be noted
that the interference fringes are not due to any interaction between the particles
coming from different slits. Indeed, the fringe pattern is independent of the
intensity of the initial beam, so that if the particles come only one at a time, they
will still avoid the dark spots and the frequency of their arrival is proportional to
the intensity (diffraction experiments with electrons coming essentially one at a
time have demonstrated this). If on the other hand, one of the slits is closed, the
fringes disappear, and one has more or less a uniform intensity. The question
that comes up is, how do the particles that are coming one at a time, know the
existence of both the slits, which persuades them to come more frequently at
the bright spots and avoid the dark spots on the screen.
The wave theory explanation of the interference pattern is that the amplitude
of the wave at any point on the screen is a superposition of the amplitude of two
66
ln Chapter 2, we have discussed some experiments which indicate that radiation
should be regarded as being made up of zero-mass particles called photons
each of which carries a quantum of energy hv and momentum
h
c
v n . It was
also observed that particles with nonzero mass, such as the electron, have wave
properties associated with them, and produce diffraction patterns similar to those
produced by radiation. Thus, a situation emerges in which radiation and matter
exhibit both particles properties, i.e., they carry quantum of energy and
momentum, and wave properties, i.e., they produce diffraction patterns.
Here, the basic laws governing the wave-particle behaviour of matter will
be analysed and applied to some simple cases. In deducing the laws, we will
borrow heavily from the wave properties of radiation and particle properties of
matter particles, with which one is familiar.
3.1 A THOUGHT EXPERIMENT
Consider a thought experiment in which a beam of particles is incident on two
closely-spaced narrow slits S 1 and S 2 , as shown in Fig. 3.1 These slits act as
two coherent sources and produce interference fringes on a screen S placed at
a distance so far away that the separation between the slits is negligible compared
to their distance from the screen. This experiment is Young’s double slit experiment
for radiation, but here it is reanalysed in terms of the particle which constitute
the beam.
The intensity variation on the screen is given by the familiar interference
fringes. The interpretation of the interference fringes in terms of the particles is
that the intensity is proportional to the number of particles arriving at various
points, with no particles coming to regions with zero intensity. It is to be noted
that the interference fringes are not due to any interaction between the particles
coming from different slits. Indeed, the fringe pattern is independent of the
intensity of the initial beam, so that if the particles come only one at a time, they
will still avoid the dark spots and the frequency of their arrival is proportional to
the intensity (diffraction experiments with electrons coming essentially one at a
time have demonstrated this). If on the other hand, one of the slits is closed, the
fringes disappear, and one has more or less a uniform intensity. The question
that comes up is, how do the particles that are coming one at a time, know the
existence of both the slits, which persuades them to come more frequently at
the bright spots and avoid the dark spots on the screen.
The wave theory explanation of the interference pattern is that the amplitude
of the wave at any point on the screen is a superposition of the amplitude of two