First slide

Photo Electric Effect

Question

When a metallic surface is illuminated with radiation of wavelength $λ$ the stopping potential is $v$ . If the same surface is illuminated with radiation of wavelength $2 λ$ the stopping potential is $\frac{V}{4}$ , The threshold wavelength for the metallic surface is

Moderate

A

$\frac{5}{2} λ$
B

$3 λ$
C

$4 λ$
D

$5 λ$

Solution

According to Einstein's photoelectric equation,
$e V_{s} = \frac{h c}{λ} - \frac{h c}{λ_{0}}$
$∴ As per question, e V = \frac{h c}{λ} - \frac{h c}{λ_{0}}$ ……..(i)
$\frac{e V}{4} = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$ ……(ii)
$F r o m e q u a t i o n s (i) a n d (i i), w e g e t$
$\frac{h c}{2 λ} - \frac{h c}{4 λ} = \frac{h c}{λ_{0}} - \frac{h c}{4 λ_{0}} \Rightarrow \frac{h c}{4 λ} = \frac{3 h c}{4 λ_{0}} or λ_{0} = 3 λ$

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