Two identical photocathodes receive light of frequencies n 1 and n 2 . If the velocities of the emitted photoelectrons of mass m are V 1 and V 2 respectively, then ( h = Planck's constant

Question

Two identical photocathodes receive light of frequencies n 1 ​ and n 2 ​ . If the velocities of the emitted photoelectrons of mass m are V 1 ​ and V 2 ​ respectively, then ( h = Planck's constant)

TestHub · Accepted Answer

Using Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectrons is given by $K = hn - W$ , where $W$ is the work function of the material.

For the first case:
$\frac{1}{2} m V_{1}^{2} = h n_{1} - W$

For the second case:
$\frac{1}{2} m V_{2}^{2} = h n_{2} - W$

Subtracting the second equation from the first, we get:
$\frac{1}{2} m V_{1}^{2} - \frac{1}{2} m V_{2}^{2} = h n_{1} - W - (h n_{2} - W)$

$\frac{1}{2} m (V_{1}^{2} - V_{2}^{2}) = h (n_{1} - n_{2})$

$V_{1}^{2} - V_{2}^{2} = \frac{2 h}{m} (n_{1} - n_{2})$

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