Chapter 7, Problem 7.15P

Interpretation Introduction

Interpretation:

The frequency and wavelength of the gamma ray emitted by the $\text{Cobalt-}60$ isotope are to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

Energy is proportional to the frequency and is expressed by the Plank-Einstein equation as follows:

$E=h\nu$

Rearrange the above equation for $\nu$.

$\nu =\frac{E}{h}$ (1)

Here,

$E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency.

The equation to relate the frequency and wavelength of electromagnetic radiation is as follows:

$\nu =\frac{c}{\lambda }$

Rearrange the above equation for $\lambda$.

$\lambda =\frac{c}{\nu }$ (2)

Here,

$c$ is the speed of light.

$\lambda$ is the wavelength.

The conversion factor to convert frequency from $\text{MeV}$ to $\text{eV}$ is,

$1\text{ MeV}={10}^6\text{ eV}$

The conversion factor to convert frequency from $\text{Hz}$ to ${\text{s}}^{-1}$ is,

$1\text{ Hz}=1{\text{ s}}^{-1}$

The conversion factor to convert energy from $\text{eV}$ to $\text{J}$ is,

$1\text{ eV}=1.6\times {10}^{-19}\text{ J}$