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A certain metallic surface is illuminated by monochromatic radiation of wavelength $λ .$ The stopping potential for photoelectric current for this radiation is $3 V_{0} .$ If the same surface is illuminated with a radiation of wavelength $2 λ,$ the stopping potential is $V_{0} .$ The threshold wavelength of this surface for photoelectric effect is____ $λ .$

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answer is 4.

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Detailed Solution

$K E = \frac{h c}{λ} - ϕ h c$

$e (3 V_{0}) = \frac{h c}{λ_{0}} - ϕ ............ (i)$

$e V_{0} = \frac{h c}{2 λ_{0}} - ϕ ............ (i i)$

Using (i) & (ii), $ϕ = \frac{h c}{4 λ_{0}} = \frac{h c}{λ_{t}}$

$λ_{t} = 4 λ_{0}$

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