First slide

Photoelectric effect and study of photoelectric effect

Question

In a photo-emissive cell, with exciting wavelength $λ$ , the maximum kinetic energy of the electron is K. If the exciting wavelength is changed to 3 $λ$ /4, the kinetic energy of the fastest emitted electron will be

Moderate

A

$\frac{3 K}{4}$
B

$\frac{4 K}{3}$
C

$less than \frac{4 K}{3}$
D

$more than \frac{4 K}{3}$

Solution

$\begin{array}{l} K = \frac{h c}{λ} - ϕ_{0} . . . . . . (i) \\ and K^{'} = \frac{4 h c}{3 λ} - ϕ_{0} . . . . . . . (i i) \end{array}$
From Eqs. (i) and (ii), we get
$\begin{array}{l} \Rightarrow K^{'} - K = \frac{4 h c}{3 λ} - \frac{h c}{λ} \\ K^{'} - K = \frac{h c}{3 λ} \\ But from Eq. (i) \frac{h c}{λ} = K + ϕ_{0} \\ ∴ K^{'} - K = \frac{K}{3} + \frac{ϕ_{0}}{3} \\ \Rightarrow K^{'} = \frac{4 K}{3} + \frac{ϕ_{0}}{3} \\ Or K^{'} > \frac{4 K}{3} \end{array}$

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