When a certain photosensitive surface is illuminated with monochr… - Vidyadip

Question

When a certain photosensitive surface is illuminated with monochromatic light of frequency $v$ , the stopping potential for the photo current is $-V_0/2.$ When the surface is illuminated by monochromatic light of frequency $v/2,$ the stopping potential is $-V_0.$ The threshold frequency for photoelectric emission is

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Answer

${\text{e}}{{\text{V}}_{\text{s}}} = {\text{hv}} - \phi $

$\left\{ {\frac{{ - e{V_0}}}{2} = hv - \phi } \right\} \times 2$ ..... $(1)$

$ - e{V_0} = \frac{{hv}}{2} - \phi $ ..... $(2)$

$0 = 2hv - 2\phi - \frac{{hv}}{2} + \phi $

$\phi = \frac{{3hv}}{2}$ $ \Rightarrow {v_{th}} = \frac{{3v}}{2}$

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