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When a certain metallic surface is illuminated with monochromatic light of wavelength $λ,$ the stopping potential for photo electric current is $6 V_{0}$ . When the same surface is illuminated with light of wavelength $2 λ,$ the stopping potential is $2 V_{0}$ . The threshold wavelength of this surface for photoelectric effect is

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$6 λ$

$4 λ / 3$

$4 λ$

$8 λ$

answer is C.

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Detailed Solution

Work function $(W) = \frac{h c}{λ_{0}}$
$6 e V_{0} = \frac{h c}{λ} - \frac{h c}{λ_{0}}$
$2 e V_{0} = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$
solving $λ_{o} = 4 λ$

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