First slide

Photoelectric effect and study of photoelectric effect

Question

Photoelectric emission is observed from a metallic surface for frequencies $v_{1}$ and $v_{2}$ of incident light $(v_{1} > v_{2})$ . If the maximum value of kinetic energies of photoelectrons emitted in these two cases are in ratio $\frac{k_{1}}{k_{2}} = \frac{1}{k}$ , then find the threshold frequency of the metal surface

Moderate

A

$\frac{k v_{1} + v_{2}}{k + 1}$
B

$\frac{k v_{1} - v_{2}}{k + 1}$
C

$\frac{k v_{2} - v_{1}}{k - 1}$
D

$\frac{k v_{1} - v_{2}}{k - 1}$

Solution

According to Einstein’s photo electric effect equation
$\begin{array}{l} {KE}_{max} = h v - ϕ \\ k_{1} = h v_{1} - ϕ; k_{2} = h v_{2} - ϕ \\ \Rightarrow \frac{k_{1}}{k_{2}} = \frac{h v_{1} - ϕ}{h v_{2} - ϕ} = \frac{1}{k} \\ \Rightarrow ϕ = \frac{h v_{1} k - h v_{2}}{k - 1} = h v_{o} \\ \Rightarrow v_{0} = \frac{k v_{1} - v_{2}}{k - 1} \end{array}$

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