Chapter U5.115, Problem 7E

Interpretation Introduction

Interpretation:

The energy of the radiation having frequency $\text{3}\times {\text{10}}^{20}{\text{ s}}^{-1}$ needs to be calculated.

Concept introduction:

The relationship between frequency and energy of the light is:

$E\propto v$

That is higher the frequency of the light, the greater is the energy of the light.

$E=hv$

Where, E is energy, h is Planck’s constant (proportionality constant) having value $6.626\times {10}^{-}{}^{34} \text{ Js}$, and v is frequency.

Answer to Problem 7E

The energy of the radiation having frequency $\text{3}\times {\text{10}}^{20}{\text{ s}}^{-1}$ is $1.9878\times {10}^{-}{}^{13} \text{ J}$.

Explanation of Solution

The frequency of the gamma radiation is $\text{3}\times {\text{10}}^{20}{\text{ s}}^{-1}$.

The formula used to calculate the energy of the gamma radiation is:

$\text{E = h}v$

Substituting the values:

$\begin{array}{l}E\text{ = }6.626\times {10}^{-}{}^{34} \text{ Js }\times \text{ 3}\times {\text{10}}^{20}{\text{ s}}^{-1}\\ E\text{ = }19.878\times {10}^{-}{}^{14} \text{ J}\\ E=1.9878\times {10}^{-}{}^{13} \text{ J}\end{array}$

Thus, the energy of the radiation having frequency $\text{3}\times {\text{10}}^{20}{\text{ s}}^{-1}$ is $1.9878\times {10}^{-}{}^{13} \text{ J}$.