Question

Explain the max planck's quantum theory and black body radiation.

Answer 1

Step 1: Definition of black body

1. Emissive power is defined as the amount of radiant energy emitted by a body per unit area of its surface per unit time.
2. The absorptive power measures the fraction absorbed of the radiant energy falling on the body.
3. If a body absorbs all the radiant energy falling on it, then its absorptive power is unity. Such a body is called a black body.
4. The emissive power of a black body is a function of temperature only.

Step 2: Max Planck's quantum theory:

According to Planck, an oscillator can have a discrete set of energies that are integral multiples of a finite quantum of energy

$\epsilon =n{\epsilon }_0=nh\nu$

where, $n$ is an integer or zero, $h$ is the Planck's constant and $\nu$ is the frequency.

Planck assumed that the change in energy of the oscillator due to emission or absorption of radiation can also take place by a discrete amount $h\nu$.

The value of $h=6.626\times {10}^{-34}Js$

Step 3: Planck's law of blackbody radiation:

1. Since radiation is emitted from the oscillators and according to Planck the change in energy of the oscillators can take place by discrete amount, the energy carried by the emitted radiation will be $h\nu$ which is equal to the loss of energy of the oscillator.
2. This is also the energy gain of the oscillator when it absorbs radiation.
3. No absorption of energy by the oscillator can take place unless the energy of the radiation $h\nu \text{'}$ is equal to the possible energy change of the oscillator $h\nu$,i.e., unless $\nu \text{'}=\nu$.
4. According to the postulates of Planck, the oscillators can exist in a set of discrete energy states $0,h\nu ,2h\nu ,3h\nu ,.....$.