Physics - Modern Physics Question with Solution | TestHub

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