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11.Dual Nature of Radiation and matter
medium
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 :
A
$3 \times 10^{16}$
B
$4.5 \times 10^{16}$
C
$4.5 \times 10^{17}$
D
$4.5 \times 10^{20}$
(JEE MAIN-2022)
Solution
Wavelength of incident beam $\lambda=900 \times 10^{-9}\,m$
Intensity of incident beam $= I =100\,W / m ^{2}$
No. of photons crossing per unit sec
$= n =\frac{ E _{\text {net }}}{ E _{\text {sim gle photon }}}=\frac{ IA \lambda}{ hc }$
$=\frac{(100)\left(1 \times 10^{-4}\right)\left(900 \times 10^{-9}\right)}{6.62 \times 10^{-34} \times 3 \times 10^{8}}=4.5 \times 10^{16}$
Standard 12
Physics
