First slide

Photo Electric Effect

Question

When a centimeter thick surface is illuminated with light of wavelength $λ$ , stopping potential is V, when the same surface is illuminated by light of wavelength 2 $λ$ , stopping potential is V /3. Threshold the same surface is illuminated by light of is

Moderate

A

$4 λ / 3$
B

$4 λ$
C

$6 λ$
D

$8 λ / 3$

Solution

$eV = hc (\frac{1}{λ} - \frac{1}{λ_{0}}) \frac{eV}{3} = hc (\frac{1}{2 λ} - \frac{1}{λ_{0}}) Dividing eq . (1) by eq . (2), we get 3 = \frac{(\frac{1}{λ} - \frac{1}{λ_{0}})}{(\frac{1}{2 λ} - \frac{1}{λ_{0}})} or 3 (\frac{1}{2 λ} - \frac{1}{λ_{0}}) = \frac{1}{λ} - \frac{1}{λ_{0}} \frac{3}{2 λ} - \frac{1}{λ} = \frac{3}{λ_{0}} - \frac{1}{λ_{0}} or \frac{1}{2 λ} = \frac{2}{λ_{0}} or λ_{0} = 4 λ$

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