First slide

Photo Electric Effect

Question

In a photo-missive cell, with exciting wavelength $λ$ the fastest electron has speed v. If the exciting wavelength is changed to $\sqrt[]{3 λ / 4}$ the speed of the fastest emitted 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

$\frac{hc}{λ_{1}} = W_{0} + \frac{1}{2} {mv}_{1}^{2} and \frac{hc}{λ_{2}} = W_{0} + \frac{1}{2} {mv}_{2}^{2} These expressions show that v^{2} \propto 1 / λ \frac{v_{1}}{v_{2}} = \sqrt{[\frac{(1 / λ_{1})}{(1 / λ_{2})}]} = \sqrt{(\frac{λ_{2}}{λ_{1}})} = \sqrt{(\frac{3 λ / 4}{λ})} = {(\frac{3}{4})}^{1 / 2} or v_{2} = v_{1} {(\frac{4}{3})}^{1 / 2}$

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