Chapter 5, Problem 71A

Interpretation Introduction

Interpretation : The energy of one photon of this radiation is to be calculated.

Concept Introduction : Planck demonstrated mathematically that a body's ability to absorb or emit radiation is inversely related to the frequency of the radiation (v). The formula of energy is given as:

  $E=h\nu$

Where, $\text{h}$ is Planck’s constant and $\nu$ is the frequency of photon.

Answer to Problem 71A

The energy of one photon of this radiation is $1.57\times {\text{10}}^{-24}\text{J}$ .

Explanation of Solution

Given information:

The frequency is $2.37\times {10}^9{\text{s}}^{-1}$ .

It is known that value of Planck’s constant is $\text{h}\text{=}6.626\times {10}^{-34}\text{J}\text{s}$ .

Planck demonstrated mathematically that a body's ability to absorb or emit radiation is inversely related to the frequency of the radiation (v).

The formula of energy is given as:

  $E=h\nu$

Where $\text{h}$ is Planck’s constant and $\nu$ is the frequency of the photon.

To calculate the energy of a photon, substitute the values in above formula.

  $\begin{array}{c}E=h\nu \\ =\left(6.626\times {10}^{-34}\text{J}\cancel{\text{s}}\right)\times \left(2.37\times {10}^9\cancel{{\text{s}}^{-1}}\right)\\ =15.70\times {10}^{-25}\text{J}\\ E=1.57\times {\text{10}}^{-24}\text{J}\end{array}$

The energy of one photon of this radiation is $1.57\times {\text{10}}^{-24}\text{J}$ .