1. The minimum energy needed by an electron to come out from a metal
surface is called the work function of the metal. Energy (greater than
the work function (fo
) required for electron emission from the metal
surface can be supplied by suitably heating or applying strong electric
field or irradiating it by light of suitable frequency.
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2. Photoelectric effect is the phenomenon of emission of electrons by metals
when illuminated by light of suitable frequency. Certain metals respond
to ultraviolet light while others are sensitive even to the visible light.
Photoelectric effect involves conversion of light energy into electrical
energy. It follows the law of conservation of energy. The photoelectric
emission is an instantaneous process and possesses certain special
features.
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3. Photoelectric current depends on (i) the intensity of incident light, (ii)
the potential difference applied between the two electrodes, and (iii)
the nature of the emitter material.
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4. The stopping potential (Vo
) depends on (i) the frequency of incident
light, and (ii) the nature of the emitter material. For a given frequency
of incident light, it is independent of its intensity. The stopping potential
is directly related to the maximum kinetic energy of electrons emitted:
e V0
= (1/2) m v
2
max
= Kmax
.
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5. Below a certain frequency (threshold frequency) n 0
, characteristic of
the metal, no photoelectric emission takes place, no matter how large
the intensity may be.
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6. The classical wave theory could not explain the main features of
photoelectric effect. Its picture of continuous absorption of energy
from radiation could not explain the independence of Kmax
on
intensity, the existence of n o
and the instantaneous nature of the
process. Einstein explained these features on the basis of photon
picture of light. According to this, light is composed of discrete
packets of energy called quanta or photons. Each photon carries an
energy E (= h n) and momentum p (= h/l), which depend on the
frequency (n ) of incident light and not on its intensity. Photoelectric
emission from the metal surface occurs due to absorption of a photon
by an electron.
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7. Einstein’s photoelectric equation is in accordance with the energy
conservation law as applied to the photon absorption by an electron in
the metal. The maximum kinetic energy (1/2)m v
2
max
is equal to
the photon energy (hn ) minus the work function f0 (= hn0
) of the
target metal:
1
2
m v
2
max
= V0
e = hn – f0 = h (n – n0)
This photoelectric equation explains all the features of the photoelectric
effect. Millikan’s first precise measurements confirmed the Einstein’s
photoelectric equation and obtained an accurate value of Planck’s
constant h. This led to the acceptance of particle or photon description
(nature) of electromagnetic radiation, introduced by Einstein.
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8. Radiation has dual nature: wave and particle. The nature of experiment
determines whether a wave or particle description is best suited for
understanding the experimental result. Reasoning that radiation and
matter should be symmetrical in nature, Louis Victor de Broglie
attributed a wave-like character to matter (material particles). The waves
associated with the moving material particles are called matter waves
or de Broglie waves.
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9. The de Broglie wavelength (l) associated with a moving particle is
related to its momentum p as: l = h/p. The dualism of matter is
inherent in the de Broglie relation which contains a wave concept
(l) and a particle concept (p). The de Broglie wavelength is
independent of the charge and nature of the material particle. It is
significantly measurable (of the order of the atomic-planes spacing
in crystals) only in case of sub-atomic particles like electrons,
protons, etc. (due to smallness of their masses and hence, momenta).
However, it is indeed very small, quite beyond measurement, in case
of macroscopic objects, commonly encountered in everyday life.
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1. Free electrons in a metal are free in the sense that they move inside the
metal in a constant potential (This is only an approximation). They are
not free to move out of the metal. They need additional energy to get
out of the metal.
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2. Free electrons in a metal do not all have the same energy. Like molecules
in a gas jar, the electrons have a certain energy distribution at a given
temperature. This distribution is different from the usual Maxwell’s
distribution that you have learnt in the study of kinetic theory of gases.
You will learn about it in later courses, but the difference has to do
with the fact that electrons obey Pauli’s exclusion principle.
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3. Because of the energy distribution of free electrons in a metal, the energy
required by an electron to come out of the metal is different for different
electrons. Electrons with higher energy require less additional energy to
come out of the metal than those with lower energies. Work function is
the least energy required by an electron to come out of the metal.
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4. Observations on photoelectric effect imply that in the event of matterlight interaction, absorption of energy takes place in discrete units of hn.
This is not quite the same as saying that light consists of particles,
each of energy hn.
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5. Observations on the stopping potential (its independence of intensity
and dependence on frequency) are the crucial discriminator between
the wave-picture and photon-picture of photoelectric effect.
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6. The wavelength of a matter wave given by h
p
λ = has physical
significance; its phase velocity vp has no physical significance. However,
the group velocity of the matter wave is physically meaningful and
equals the velocity of the particle.
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