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

Question

Infinity Learn · Accepted Answer

ω$$=Kmor$$Ω$$=KMMomentum$$ change for single photon $$=2h$$λ  Momentum change for all photons $$=$$  $$2Nh$$λMaximum velocity of $$mirror=A$$ω$$=A$$Ω​Momentum delivered to mirror by $$photons=MV=2Nh$$λ​⇒MAΩ$$=2Nh$$λ​⇒$$24$$$$π$$MΩh×$$10$$−$$12=2N$$​⇒$$N=1$$×$$1012$$

Electromagnetic radiation - Dual nature of radiation and matter

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Electromagnetic radiation - Dual nature of radiation and matter

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

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