Chapter 5, Problem 53A

Interpretation Introduction

Interpretation:

A photon has an energy of $1.10\times {10}^{-13}J$. The photon’s wavelength and type of electromagnetic radiation needs to be calculated.

Concept introduction:

Light and other forms of radiant energy propagate without any medium in the space in the form of waves are known as electromagnetic radiations.

$E=hv$, Where $E$ is energy of photon.

Answer to Problem 53A

Wave length of photon $=18.07{\times }^{-13}m$ and type of electromagnetic radiation is gamma $\left(\gamma \right)$ radiation.

Explanation of Solution

Given information:

Energy of photon $=1.10\times {10}^{-13}Joule$

Calculation:

The energy is related to frequency and wavelength as follows:

$E=hv$

$E=h\frac{c}{\lambda }$

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

Where

$\lambda =$ Wave length,

$h=$ plank’s constant $\left(6.626\times {10}^{-34}Js\right)$.

$c=$ velocity of light

$E=$ energy of photon

Putting the values,

$\begin{array}{l}\lambda =\frac{6.626\times {10}^{-34}Js\times 3.0\times {10}^{8}m/s}{1.10\times {10}^{-13}J}\\ \lambda =\frac{6.626\times 3\times {10}^{-34+8+13}}{1.1}\\ \lambda =18.07\times {10}^{-13}m\end{array}$

Wave length of photon $=18.07\times {10}^{-13}m$

Type of electromagnetic radiation is gamma $\left(\gamma \right)$ rays.