First slide

Photoelectric effect and study of photoelectric effect

Question

When photons of wavelength $λ_{1}$ are incident on an isolated sphere suspended by an insulated thread, the corresponding stopping potential is found to be Z. When photons of wave length $λ_{2}$ are used, the corresponding stopping potential was thrice the above value. If light of wavelength $λ_{3}$ is used, calculate the stopping potential for this case.

Moderate

A

$\frac{h c}{e} [\frac{1}{λ_{3}} + \frac{1}{2 λ_{2}} - \frac{1}{λ_{1}}]$
B

$\frac{h c}{e} [\frac{1}{λ_{3}} + \frac{1}{2 λ_{2}} - \frac{3}{2 λ_{1}}]$
C

$\frac{h c}{e} [\frac{1}{λ_{3}} + \frac{1}{λ_{2}} - \frac{1}{λ_{1}}]$
D

$\frac{h c}{e} [\frac{1}{λ_{3}} - \frac{1}{λ_{2}} - \frac{1}{λ_{1}}]$

Solution

$\begin{array}{rcl} {KE}_{λ_{1}} & = & \frac{h c}{λ_{1}} - ψ = e Δ V \\ {KE}_{λ_{2}} & = & \frac{h c}{λ_{2}} - ψ = 2 e Δ V \end{array}$
$\Rightarrow 3 (\frac{h c}{λ_{1}} - ψ) = \frac{h c}{λ_{2}} - ψ$
$\Rightarrow ψ = h c (\frac{3}{2 λ_{1}} - \frac{1}{2 λ_{2}})$
$\begin{array}{rcl} \Rightarrow & {KE}_{λ_{3}} = \frac{h c}{λ_{3}} - h c [\frac{3}{2 λ_{1}} - \frac{1}{2 λ_{2}}] \\ = & h c [\frac{1}{λ_{3}} + \frac{1}{2 λ_{2}} - \frac{3}{2 λ_{1}}] \\ e Δ V & = & h c [\frac{1}{λ_{3}} + \frac{1}{2 λ_{2}} - \frac{3}{2 λ_{1}}] \\ Δ V & = & \frac{h c}{e} [\frac{1}{λ_{3}} + \frac{1}{2 λ_{2}} - \frac{3}{2 λ_{1}}] \end{array}$

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