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# 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