Question

A metal surface experiences ${10}^{-8}\text{N}$ force due to radiation. If its area exposed to radiations is $2{\text{m}}^2$, calculate the wavelength of the radiation (in $\mu \text{m})$.
$($Given: No. of photons incident per second $=5\times {10}^{12})$

• A. $0.08$
• B. $0.8$
• C. $0.5$
• D. $0.05$

Answer 1

The correct option is C $0.5$

The no. of incident photons is, $n=\frac{IA\lambda }{hc}---\left(1\right)$ per second
Also, radiation pressure is, $P=\frac{F}{A}=\frac{I}{c}$
$\therefore \frac{I}{c}=\frac{F}{A}---\left(2\right)$

Putting $\left(2\right)$ in $\left(1\right)$,
$n=\frac{A\lambda }{h}\frac{I}{c}$
$\Rightarrow 5\times {10}^{12}=\frac{2\times \lambda }{6.63\times {10}^{-34}}\times \frac{{10}^{-8}}{3\times {10}^8}$

$\lambda =4.965\times {10}^{-5}\text{m}\approx 0.4\mu \text{m}$

Hence, $\left(C\right)$ is the correct answer.