A parallel beam of light of wavelength 900   nm and intensity 100 Wm - 2 is incident on a surface…

A parallel beam of light of wavelength 900 nm and intensity 100Wm-2 is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm2 area perpendicular to the beam in one second is
  1. 3×1016
  2. 4.5×1016
  3. 4.5×1017
  4. 4.5×1020

Solution

Wavelength of incident beam λ=900×10-9 m

Energy of a single photon E=hcλ.

Intensity is defined as power per unit area. Therefore,

Intensity of incident beam I=EtA

If the number of photons crossing the given area per second is n, then

n=Enet Esingle pholon =IAλhc

n=1001×10-4900×10-96.62×10-34×3×108=4.5×1016.

Asked in: JEE Main 2022 (26 Jul Shift 1)

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