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.
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
(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