NCERT Class 12 Physics Part-2 Solutions | Content | English Medium

  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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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  1. 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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