When a metallic surface is illuminated with a radiation of wavelength ' λ ', the stopping potential is ' V '. If' the same surface is illuminated with radiation of wavelength

Question

When a metallic surface is illuminated with a radiation of wavelength ' λ ', the stopping potential is ' V '. If' the same surface is illuminated with radiation of wavelength ' 3 λ ', the stopping potential is " ( 6 V ​ ) '. The threshold wavelength for the surface is

TestHub · Accepted Answer

Using Einstein's photoelectric equation:

$e V = \frac{h c}{λ} - \frac{h c}{λ _{0}}$

For the first case:

$e V = \frac{h c}{λ} - \frac{h c}{λ _{0}}$

For the second case:

$\frac{e V}{6} = \frac{h c}{3 λ} - \frac{h c}{λ _{0}}$

Multiplying the second equation by $6$ :

$e V = \frac{2 h c}{λ} - \frac{6 h c}{λ _{0}}$

Equating the two expressions for $e V$ :

$\frac{h c}{λ} - \frac{h c}{λ _{0}} = \frac{2 h c}{λ} - \frac{6 h c}{λ _{0}}$

Rearranging the terms:

$\frac{6 h c}{λ _{0}} - \frac{h c}{λ _{0}} = \frac{2 h c}{λ} - \frac{h c}{λ}$

$\frac{5 h c}{λ _{0}} = \frac{h c}{λ}$

$λ_{0} = 5 λ$

Answer: $5 λ$

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