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

MCQ

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

A
$\frac {5v}{3}$
B
$\frac {4}{3}\,v$
C
$2\,v$
✓
$\frac {3v}{2}$

✓

Answer

Correct option: D.

$\frac {3v}{2}$

d
${\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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