A beam of light whose intensity is 1 µW cm-2 and whose wavelength is 400 nm fall

Question

A beam of light whose intensity is 1 µW cm-2 and whose wavelength is 400 nm falls on a metal plate whose work function is 2 eV.
Light of this wavelength readily ejects photoelectrons from the plate and they appear as soon as the beam is switched on.
Now suppose that classical theory applies to the photo-electric effect.
How long would the beam of light need to shine on an atom (cross-sectional area has radius of about 10-10 m) for a total energy of 2 eV to be delivered to the atom by the beam?
This is the minimum time, according to classical theory, in which an electron could acquire enough energy to be flung free of the atom.

Explanation / Answer

SOLUTION The average power Pav selivered by the wave of intensity I to an area A is IA. An atom on the surface displays a target area of A = r2 = (10-10 m) 2= 3.14 (10-20 m2 ). If the entire electromagnetic power is delivered to the electrons , energy is absorbed at the rate E /t = P av. The inervel t necessary to absorb an energy E = can be expressed t = (E) / (P av) = / I A here = 2 eV (1.6 x 10-19 J / eV) Therefore t = [ 2 eV (1.6 x 10-19 J / eV) ] /   [ (1 µW cm-2 ) ( 3.14 (10-20 m2 ).]                     =[ 2 eV (1.6 x 10-19 J / eV) ] / [ 1 x 10-2 W / m2 ) (3.14 (10-20 m2 ).]                     =1.019 x 103 s                   =1019 s                   =1019 s

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