Question

Explain Planck's Quantum theory.

Answer 1

Hint: Planck gave the quantum theory in 1900, the theory consists of radiation getting absorbed and emitted by atoms of different elements. He also found out that the energy of the radiation emitted or absorbed by the atom is directly proportional to the frequency.

Complete Step By Step Answer:
Planck developed the quantum theory in 1900 and it describes that the energy of radiation getting emitted or getting absorbed by an atom is not consistent or continuous. Instead, the energy can be emitted or absorbed in discrete quantities.
These discrete quantities come in a small bundle of energy to the atom, they are called quanta and in terms of light, they are called photons. Atoms emit or absorb energy only in terms of these small bundles of energies.
Another thing that was proved in quantum theory by Planck was that the energy of each quanta or photon is directly proportional to its own frequency. If $ E $ represents energy of the quanta and $ v $ represents the frequency, then $ E $ is directly proportional to $ v $ .
 $ \Rightarrow $ $ E\propto v $
After adding the equality constant, the equation looks like this.
 $ \Rightarrow $ $ E=hv $
Here, $ h $ represents Planck’s constant, the value of Planck’s constant is $ 6.626\times {{10}^{-34}}Js $ . The unit of Planck’s constant is joule second.
As we know that frequency is the speed of light in vacuum divided by the wavelength of the quanta. Thus,
 $ \Rightarrow $ $ E=\dfrac{hc}{\lambda } $
Where, $ \lambda $ is the wavelength of the quanta and $ c $ is the speed of light in vacuum.
The formula $ E=hv $ is only for one quanta or photon, thus it is called quantum. Energy of the radiation will be in proportion with the quanta in terms of the whole number. Thus, the total amount of energy absorbed or emitted is the integral multiple of the energy of a single photon.
Therefore, $ E=nhv $ , where $ n $ represents a whole number.
Thus, this is Planck’s quantum theory.

Note:
The quantum theory given by Planck for emission and absorption of the radiation is only for the process of radiation. The physical reality is not connected with the process given by Planck, this was concluded by Planck. The quantum theory was used by Albert Einstein later to explain the photoelectric effect.