First slide

Photo Electric Effect

Question

In photo-emissive cell, with exciting wavelength λ, the fastest electron has speed v. If the exciting wavelength is changed to 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

Einstein's photoelectric equation is given by
$E_{k} = E - w$
$but E_{k} = \frac{1}{2} {mv}^{2} and E = \frac{ch}{λ}$
$∴ \frac{1}{2} {mv}^{2} = \frac{ch}{(3 λ / 4)} - w$
$or \frac{1}{2} m v^{2} = \frac{4}{3} \frac{h c}{λ} - w \dots (2)$
Dividing Eq. (ii) by Eq. (i), we get
$\frac{v^{2}}{v^{2}} = \frac{\frac{4}{3} \frac{ch}{λ} - w}{\frac{ch}{λ} - w}$
$= \frac{\frac{4}{3} \frac{ch}{λ} - \frac{4}{3} w + \frac{1}{3} w}{\frac{ch}{λ} - w}$
$= \frac{4}{3} + \frac{w}{3 (\frac{ch}{λ} - w)} > \frac{4}{3}$
$∴ \frac{v^{2}}{v^{2}} > \sqrt{\frac{4}{3}} or v^{'} > \sqrt{\frac{4}{3}} v$

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