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A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency Ω such that 4πMΩh=1024m−2 with h as Planck’s constant. N photons of wavelength λ=8π×10−6m strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1μm . If the value of N is x ×1012, then the value of x is ______[Consider the spring as massless]

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Detailed Solution

ω=KmorΩ=KMMomentum change for single photon =2hλ Momentum change for all photons = 2NhλMaximum velocity of mirror=Aω=AΩMomentum delivered to mirror by photons=MV=2Nhλ⇒MAΩ=2Nhλ⇒24πMΩh×10−12=2N⇒N=1×1012

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A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency Ω such that 4πMΩh=1024m−2 with h as Planck’s constant. N photons of wavelength λ=8π×10−6m strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1μm . If the value of N is x ×1012, then the value of x is ______[Consider the spring as massless]