Question

A body of mass $m$ emits a photon of frequency $v$, then loss in its internal energy?

• A. $h\nu$
• B. $h\nu (1-\frac{h\nu }{2m{c}^2})$
• C. $h\nu (1+\frac{h\nu }{2m{c}^2})$
• D. Zero

Answer 1

The correct option is C

$h\nu (1+\frac{h\nu }{2m{c}^2})$

Step 1.Given Data:

1. Mass, $m$
2. Frequency, $\nu$

Step 2. Formula Used: $Momentum\propto frequencyandinverseofwavelength$

Step 3. Calculation of momentum of photon:

$mV=h\nu /c$

where, $V$ is the velocity of the photon and $c$ is speed of light.

Step 4. Calculation of loss of internal energy:

$$\begin{gathered} \frac{1}{2}m{V}^2+h\nu \\ =\frac{1}{2}m{\left(\frac{h\nu }{mc}\right)}^2+h\nu \\ =\frac{1}{2m}{\left(\frac{h\nu }{c}\right)}^2+h\nu \\ =h\nu (1+\frac{h\nu }{2m{c}^2}) \end{gathered}$$

Hence, option C is the correct answer.