Mirror on a spring

JEE Advanced 2019 Paper 2, Question 12

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} \, {\rm m}^{-2} with h as Planck’s constant. N photons of wavelength \lambda = 8 \pi \times 10^{-6} \, {\rm m} strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1 \mu{\rm m}.
If the value of N is x \times 10^{12}, what is the value of x?

[Consider the spring as massless]

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The momentum carried by a single photon is given by the de Broglie relation p_{\rm ph} = h/\lambda. The total momentum carried by N photons is therefore N \times p_{\rm ph} = Nh/\lambda. All the photons hit the mirror simultaneously and are reflected …

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