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  4. A parallel beam of light of wavelength 900 nm and intensity 100 Wm -2 is incident on a surface perpendicular to the beam. Tire number of photons crossing 1 cm 2 area perpendicular to the beam in one second is :

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Q. A parallel beam of light of wavelength $900 \,nm$ and intensity $100 \,Wm ^{-2}$ is incident on a surface perpendicular to the beam. Tire number of photons crossing $1 \,cm ^2$ area perpendicular to the beam in one second is :

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Solution:

Wavelength of incident beam $\lambda=900 \times 10^{-9}$
Intensity of incident beam $= I =100 W / m ^2$
No. of photons crossing per unit sec
$ = n =\frac{ E _{\text {net }}}{ E _{\text {single photon }}}=\frac{ IA \lambda}{ hc } $
$ =\frac{(100)\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}$