```PLANCK’S QUANTUM THEORY
When a black body is heated, it emits thermal radiations of different wavelengths or frequency. To explain these radiations, Max Planck put forward a theory known as Planck’s quantum theory. The main points of quantum theory are

Substances radiate or absorb energy discontinuously in the form of small packets or bundles of energy.

The smallest packet of energy is called quantum. In case of light the quantum is known as photon.

The energy of a quantum is directly proportional to the frequency of the radiation. E µ n (or) E = hn where n is the frequency of radiation and h is Planck’s constant having the value 6.626 X 10–27 erg – sec or 6.626 X 10–34 J–sec.

A body can radiate or absorb energy in whole number multiples of a quantum hn, 2hn,3hn………..nhn. Where ‘n' is the positive integer.

Neils Bohr used this theory to explain the structure of atom.

Illustration: The wave number of a radiation is 400 cm-1. Find out its
(a) Wavelength                         (b) Frequency
(c) J per photon                        (d) kcal per mol of photons
(e)KJ per mol of photons

Solution:
(a) v- = 1 / λ or λ = 1 / v- =  1 / 400cm-1 = 2.5 x 10–3 cm
(b) v = c / λ  =  c x v- = 3 x 10–10 cm/s x 400 cm–1 = 1.2 x 10-7 s-1
(c)  Ephoton = hn = hc / λ  = h x c x v-
= 6.626 x 10–34 Js x 3 x 108 cm/s x 400 cm–1
= 7.95 x 10–21J
(d) Ephoton   = 7.95 x 10–21J
For 1 mol of photon energy = 7.95 x 10–21J x 6.022 x 1023 mol–1
= (4.7875 x 103 J mol–1) (1 kcal/4184 J)
= 1.14 kcal mol–1
(e) E = (4.7875 x 103 J mol–1) (1 kJ/1000J)
= 4.7875 kJ mol–1 ```
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