Chapter 5.1, Problem 11SSC

Interpretation Introduction

Interpretation:

The quantum theory needs to be employed to assess the amount of energy that matter gains and losses.

Concept introduction:

The black body emits or absorbs radiant energy in the form of small packets called quantum. This energy is discontinuous in nature.

Explanation of Solution

According to quantum theory, matter and light both are composed of tiny particles having wave-like properties. Light has tiny particles called photons and matter has electrons, protons and neutrons.

The energy emitted or absorbed by a black body is discontinuous and in the form of small packets called quantum. Here, the single quantum is the minimum energy that can be gained or lost by an atom. Thus, it can be said that matter gains or losses energy as multiples of quantum.

In the case of light, the quantum of energy is called a photon.

The energy of each quantum is directly proportional to the frequency ( $\nu$ ) of the radiation, i.e., $E\propto \nu$

Or,

$E=hv=\frac{hc}{\lambda }$

Where, $h=$ Planck's constant = $6.62\times {10}^{-34}\text{J s}$

Thus, the total energygained or lost by a body can be represented as a whole number quantum. Hence,

$E=nh\nu$

Here, n is an integer.