Question

A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $\omega $ such that $\frac{4 \pi M \omega }{h}=10^{24}m^{- 2}$ with $h$ as Planck's constant. $N$ photons of wavelength $\lambda =8\pi \times 10^{- 6}m$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1\,\mu m$ . If the value of $N$ is $x\times 10^{12}$ . Then the value of $x$ is [Consider the spring as massless]

Answer 1

$mV _{\max }=\left(\frac{2 h }{\lambda}\right) N$
$m\cdot \omega A=\frac{2 h}{\lambda }N$
$N=\frac{m \omega \lambda A}{2 h}$
$N=\frac{10^{24}}{4 \pi} \times \frac{8 \pi \times 10^{-6}}{2}\left(10^{-6}\right)$
$N=10^{12}$
$\therefore x=1$