First slide

Photoelectric effect and study of photoelectric effect

Question

In a photocell, with excitation wavelength $λ$ , the faster electron has speed v. If the excitation wavelength is changed to $3 λ / 4$ , the speed of the fastest electron will be

Moderate

A

$v (3 / 4)^{1 / 2}$
B

$v (4 / 3)^{1 / 2}$
C

$less than v (4 / 3)^{1 / 2}$
D

$greater than v (4 / 3)^{1 / 2}$

Solution

$\frac{1}{2} m v^{2} = \frac{h c}{λ} - W_{0} . . . . . . . . . (i)$
Let the speed of the fastest electron be V₁ when excitation wavelength is changed to $3 λ / 4$
$\begin{array}{l} ∴ \frac{1}{2} m v_{1}^{2} = \frac{4 h c}{3 λ} - W_{0} \\ \Rightarrow \frac{1}{2} m v_{1}^{2} = \frac{4}{3} (\frac{h c}{λ} - W_{0}) + \frac{W_{0}}{3} \\ \Rightarrow \frac{1}{2} m v_{1}^{2} = \frac{4}{3} (\frac{1}{2} m v^{2}) + \frac{W_{0}}{3} [u \sin g E q . (i)] \\ \Rightarrow v_{1}^{2} = \frac{4 v^{2}}{3} + \frac{2 W_{0}}{3 m} \\ ∴ v_{1} > \sqrt{\frac{4}{3}} v \end{array}$

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