Two identical photocathodes receive the light of frequencies f 1 and f 2 respectively. If the velocities of…

Two identical photocathodes receive the light of frequencies

f_{1}

and

f_{2}

respectively. If the velocities of the photo-electrons coming out are

v_{1}

and

v_{2}

respectively, then

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

Solution

$\frac{1}{2} m v_{1}^{2} = h f_{1} - ϕ$

$\frac{1}{2} m v_{2}^{2} = h f_{2} - ϕ$

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

Asked in: JEE Main 2021 (17 Mar Shift 2)

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