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Question

Find the frequency of light which ejects electrons from a metal surface, fully stopped by a retarding potential of 3.3V. If photo electric emission begins in this metal at a frequency of 8×1014Hz, calculate the work function (in eV) for this metal.

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Solution

Given that;
Stoping potential, vs=3.3v
Minimum frequency needed to eject electrons from metal= frequency for work function =νTh=threshold frequency
νTh=8×1014Hz
ϕ= work function =hνTh=6.62×1034×8×1014
ϕ=5.296×1019J
1.6×1019J=1eV
ϕ=5.296×10191.6×1019=3.31eV
Work function for the metal =ϕ=3.31eV
Use Einstein equation:-
Incident energy, E=ϕ+evs
E=(3.31+3.3)eV
E=6.61ev=(6.61×1019×1.6)J
E=hν=6.61×1.6×1019
ν=6.61×1.6×10196.62×1034=1.6×1015Hz
Thus, frequency of light =ν=1.6×1015Hz.

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