Planck’s Quantum Theory of Radiation| Black body radiation

Planck’s Quantum Theory of Radiation:

In 1900, a German Physicist Max Planck had studied radiations emitted by hot black bodies and presented the results of his famous black body radiations experiments, which showed that light has a dual character, behaving like a particle as well as a wave.

He gave the quantum theory of radiation explaining electromagnetic radiation and energy.

Main Postulates of Planck’s theory:

1. Energy radiated by hot bodies is not continuous, rather it is emitted in the form of small “energy packets” or “energy pulses” known as quanta (singular is quantum). In the case of light, the quantum of energy is called a photon.

2. Each quantum has a definite amount of energy.

3. This energy of the quantum is directly proportional to the frequency of radiations.

E ∝ ﬠ

Or    E = h ﬠ

4. According to Planck, energy of a quantum or photon is given as:

E     =   hﬠ          

  Where

E = energy

h = Planck’s constant   = 6.6262 x 10^-34 J.s

  ﬠ  = frequency of radiation

But      ﬠ   =    c / λ                                                    

So        E    =  hc / λ ………………. (2)                    

Equation-1 shows that the energy of quanta or photon is directly proportional to the frequency of radiations emitted or absorbed.

    E ∝  ﬠ

 While equation-2 shows that the energy of quanta or photon is inversely proportional to the wavelength of radiations.

E ∝ 1 /λ

1.  The energy emitted or absorbed by a body is always whole number multiple of quantum and never in fraction. i.e.                   

  E_n = n h ﬠ   

  where n = 1, 2, 3,……..

This means energy is quantized.

The energy of a photon can also be given as

According to Planck,  E = hﬠ

   We know the frequency of radiation is inversely proportional to its wavelength.                     

   Putting in equation (1)

E = h c/ λ                     

    or             

E = hc x 1/ λ ………………….. (2)

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