Dual Nature of Matter

JEE Main level, single correct, medium

143 of 200

Question 143 of 200

A parallel beam of light of wavelength 900nm900nm and intensity 100Wm−2100{Wm}^{-2} is incident on a surface perpendicular to the beam. The number of photons crossing 1cm21{cm}^{2} area perpendicular to the beam in one second is

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Answer: (B) 4.5×10164.5\times {10}^{16}

Wavelength of incident beam λ=900×10−9m\lambda =900\times {10}^{-9}m
Energy of a single photon E=hcλE=\dfrac{hc}{\lambda }.
Intensity is defined as power per unit area. Therefore,
Intensity of incident beam I=EtAI=\dfrac{E}{tA}
If the number of photons crossing the given area per second is nn, then
n=EnetEsinglepholon=IAλhcn=\dfrac{{E}_{net}}{{E}_{singlepholon}}=\dfrac{IA\lambda }{hc}
⇒n=(100)(1×10−4)(900×10−9)6.62×10−34×3×108=4.5×1016\Rightarrow n=\dfrac{\left(100\right)\left(1\times {10}^{-4}\right)\left(900\times {10}^{-9}\right)}{6.62\times {10}^{-34}\times 3\times {10}^{8}}=4.5\times {10}^{16}.

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