Question

Calculate the frequency in hertz of a \(1.00 - MeV\)\(\gamma \)-ray photon.

Short answer

The frequency in hertz of a \(1.00{\rm{ }}MeV\)\(\gamma \)- ray of photon is, \(f = 2.42 \times {10^{20}}\;Hz\)

Step-by-step solution

Concept Introduction

The frequency of a sinusoidal wave is the number of full oscillations performed by any wave component in one unit of time. The concept of frequency can be used to understand that if a body is in periodic motion, it has finished one cycle after going through a sequence of experiences or locations and returning to its initial state. As a result, frequency is a term used to indicate how frequently oscillations and vibrations take place.

Information Provided

• Energy of \(\gamma \)- ray of photon is: \(\begin{aligned}E = 1.00{\rm{ }}MeV\\ = 1.00 \times {10^6}{\rm{ }}eV\end{aligned}\)

Calculation for Frequency

The energy of a photon is given by –

\(E = hf......(1)\)

Where\(h = 6.626 \times {10^{ - 34}}Js\), is Planck's constant, and\(f\)is the frequency of the incident photon.

Since, it is known that –

\(1.00\;J = 6.242 \times {10^{18}}{\rm{ }}eV\)

Hence, it is obtained that –

\(\begin{aligned}E = 1.00 \times {10^6}eV \times \dfrac{{1.00\;J}}{{6.242 \times {{10}^{18}}eV}}\\ = 1.602 \times {10^{ - 13}}\;J\end{aligned}\)

So, now from equation\((1)\), it is obtained –

\(\begin{aligned}f &= \dfrac{E}{h}\\ &= \dfrac{{1.602 \times {{10}^{ - 13}}\;J}}{{6.626 \times {{10}^{ - 34}}Js}}\\ &= 2.42 \times {10^{20}}\;Hz\end{aligned}\)

Therefore, the value for frequency is obtained as\(f = 2.42 \times {10^{20}}\;Hz\).