First slide

Photo Electric Effect

Question

Two identical photo-cathodes receive light of frequencies $f_{1} and f_{2}$ . If the velocities of the photo electrons (of mass m ) coming out are respectively $v_{1} and v_{2}$ , then

Moderate

A

$v_{1} - v_{2} = {[\frac{2 h}{m} (f_{1} - f_{2})]}^{1 / 2}$
B

$v_{1}^{2} - v_{2}^{2} = \frac{2 h}{m} (f_{1} - f_{2})$
C

$v_{1} + v_{2} = {[\frac{2 h}{m} (f_{1} + f_{2})]}^{1 / 2}$
D

$v_{1}^{2} + v_{2}^{2} = \frac{2 h}{m} (f_{1} + f_{2})$

Solution

Using Einstein photoelectric equation
$\begin{array}{l} E = W_{o} + K_{\max} \\ {hf}_{1} = W_{o} + \frac{1}{2} {mv}_{1}^{2} . . . (i) \\ {hf}_{2} = W_{o} + \frac{1}{2} {mv}_{2}^{2} . . . (ii) \\ \Rightarrow h (f_{1} - f_{2}) = \frac{1}{2} mv (v_{1}^{2} - v_{2}^{2}) \\ \Rightarrow (v_{1}^{2} - v_{2}^{2}) = \frac{2 h}{m} (f_{1} - f_{2}) \end{array}$

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