Question

The laser beam of wavelength, $\lambda =5\times {10}^{-7}m$ strikes normally on a blackened plate and produces a force of ${10}^{-5}N$.
Mass of plate is $10g$ and its specific heat capacity is $400Jk{g}^{-1}{K}^{-1}$ . The temperature rise of plate per second is $xK$. Then the value of $\frac{x}{100}$ is (Answer upto two digits after decimal point)

Answer 1

Force = change in momentum of one photon $\times$ number of photons striking per second
$\Rightarrow {10}^{-5}=\frac{hn}{\lambda }=\frac{hc}{\lambda }\frac{n}{c}=\frac{E}{c}$
$\text{E}\to$ energy incident per second.
Now, $ms\frac{d\theta }{dt}=c\times {10}^{-5}=3\times {10}^3\Rightarrow \frac{d\theta }{dt}=\frac{3\times {10}^3}{10\times {10}^{-3}\times 400}=750{\text{K s}}^{-1}$