Introduction to Quantum Ideas
39
the photoelectric effect. It explains all the observed features of photoelectric
effect. It should be noted that
1. Since photons are absorbed as single units, there is a localization of energy
and hence there is no significant time delay in the emission of electrons.
2. Einstein’s relation in Eq. (2.23) implies the existence of a critical frequency
for the emission of electrons, given by
0
e
v
h
φ
=
(2.24)
However, since the current increases gradually as V increases from –V 0 ,
the effective binding of the electrons inside the metal varies as also the
velocity of the emitted electrons. Therefore, the critical frequency in
Eq. (2.24) refers to the emission of electrons with minimum binding energy.
3. The maximum kinetic energy of the emitted electrons (having minimum
binding energy) is given in terms of the critical frequency, by the relation
2
0
1
(
)
2
m
mv
h v v
=
−
(2.25)
In terms of the stopping potential V 0 , one has
eV 0 = h (v–v 0 )
(2.26)
Thus, it not only explains all the experimental observations but also gives the
ratio of h/e from the slope of the linear plot of V 0 against v. Using the known
value for the charge of the electron, an independent determination of Planck’s
constant, in good agreement with the value obtained from other considerations
such as the black-body radiation, can be obtained.
Some additional observations related to the photoelectric effect are:
1. Only a small fraction (about 5%) of the incident photons, succeeds in
ejecting photoelectrons while most of them are absorbed by the system as
a whole and generate thermal energy.
2. Photoelectric effect is also possible for isolated atoms in the form of a gas,
e.g. Na, K vapour, and the process is known as photoionization. It is
observed by passing a beam of ultraviolet radiation through a chamber
containing Na or K vapour, and collecting the electrons ejected by subjecting
them to an electric field. It is interesting to not that in photoionization, since
the atoms are isolated, there is no collective absorption of photons and
every photon absorbed succeeds in ejecting an electron. This can be verified
by comparing the number of photons absorbed as deduced from the
decrease in the intensity of the beam, with the number of electrons collected
by the electric field.
39
the photoelectric effect. It explains all the observed features of photoelectric
effect. It should be noted that
1. Since photons are absorbed as single units, there is a localization of energy
and hence there is no significant time delay in the emission of electrons.
2. Einstein’s relation in Eq. (2.23) implies the existence of a critical frequency
for the emission of electrons, given by
0
e
v
h
φ
=
(2.24)
However, since the current increases gradually as V increases from –V 0 ,
the effective binding of the electrons inside the metal varies as also the
velocity of the emitted electrons. Therefore, the critical frequency in
Eq. (2.24) refers to the emission of electrons with minimum binding energy.
3. The maximum kinetic energy of the emitted electrons (having minimum
binding energy) is given in terms of the critical frequency, by the relation
2
0
1
(
)
2
m
mv
h v v
=
−
(2.25)
In terms of the stopping potential V 0 , one has
eV 0 = h (v–v 0 )
(2.26)
Thus, it not only explains all the experimental observations but also gives the
ratio of h/e from the slope of the linear plot of V 0 against v. Using the known
value for the charge of the electron, an independent determination of Planck’s
constant, in good agreement with the value obtained from other considerations
such as the black-body radiation, can be obtained.
Some additional observations related to the photoelectric effect are:
1. Only a small fraction (about 5%) of the incident photons, succeeds in
ejecting photoelectrons while most of them are absorbed by the system as
a whole and generate thermal energy.
2. Photoelectric effect is also possible for isolated atoms in the form of a gas,
e.g. Na, K vapour, and the process is known as photoionization. It is
observed by passing a beam of ultraviolet radiation through a chamber
containing Na or K vapour, and collecting the electrons ejected by subjecting
them to an electric field. It is interesting to not that in photoionization, since
the atoms are isolated, there is no collective absorption of photons and
every photon absorbed succeeds in ejecting an electron. This can be verified
by comparing the number of photons absorbed as deduced from the
decrease in the intensity of the beam, with the number of electrons collected
by the electric field.