When a certain metallic surface is illuminated with monochromatic light wavelength λ , the stopping potential for photoelectric current is 4 V 0 . When the same surface is illuminated with light of

Question

When a certain metallic surface is illuminated with monochromatic light wavelength λ , the stopping potential for photoelectric current is 4 V 0 ​ . When the same surface is illuminated with light of wavelength 3 λ , the stopping potential is V 0 ​ . The threshold wavelength for this surface for photoelectric effect is

TestHub · Accepted Answer

According to Einstein's photoelectric equation:

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

For the first case:

$4 e V_{0} = \frac{h c}{λ} - \frac{h c}{λ _{0}}$

For the second case:

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

Multiplying the second equation by $4$ and equating with the first equation:

$\frac{h c}{λ} - \frac{h c}{λ _{0}} = 4 (\frac{h c}{3 λ} - \frac{h c}{λ _{0}})$

Dividing by $h c$ on both sides:

$\frac{1}{λ} - \frac{1}{λ _{0}} = \frac{4}{3 λ} - \frac{4}{λ _{0}}$

Rearranging the terms:

$\frac{4}{λ _{0}} - \frac{1}{λ _{0}} = \frac{4}{3 λ} - \frac{1}{λ}$

$\frac{3}{λ _{0}} = \frac{1}{3 λ}$

$λ_{0} = 9 λ$

Answer: $9 λ$

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