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Question

A beam of electromagnetic radiation of intensity 6.4× 105 W/cm2 is comprised of wavelength, λ=310 nm. It falls normally on a metal (work function ϕ=2 eV) of surface area 1 cm2. If one in 103 photons ejects an electron, total number of electrons ejected in 1s is 10x (hc=1240 eVnm,1 eV=1.6×1019 J), then x is

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Solution

P=Intensity×Area=6.4×105Wcm2×1 cm2=6.4×105 W
For photoelectric effect to take place, energy should be greater than work function
Now,
E=1240310=4 eV>2 eV
Therefore, photoelectric effect takes place
Here n is the number of photons emitted.

n×E=I×An=IAE=6.4×1056.4×1019=1014
Where, n is number of incident photon
Since, 1 out of every 1000 photons are sucessfull in ejecting 1 photoelectron
Therefore, the number of photoelectrons emitted is
=1014103
x=11

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