A certain metallic surface is illuminated with monochromatic light of wavelength A. The stopping potential for photo-electric current for this light is 3V₀ • If the same surface is illuminated with light of wavelength 2 $λ$ the stopping potential is V₀ • The threshold wavelength for this surface for photo-electric effect is

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$4 λ$

$\frac{λ}{4}$

$\frac{λ}{6}$

$6 λ$

answer is A.

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Detailed Solution

As we know,

$\begin{array}{l} {eV}_{s} = \frac{hc}{λ} - Ψ \\ 3 {eV}_{o} = \frac{hc}{λ} - Ψ \dots (1) \\ {eV}_{o} = \frac{hc}{2 λ} - Ψ \dots (2) \\ 3 {eV}_{o} = \frac{3 hc}{2 λ} - 3 Ψ \dots \end{array}$

Multiplying eqn. (2) by (3) and subtracting it from eqn (1)

$Ψ = \frac{h}{4 λ}$

So,threshold wavelength,

$λ_{th} = \frac{hc}{Ψ} = \frac{hc}{\frac{hc}{4 λ}} = 4 λ$

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