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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