First slide

Photoelectric effect and study of photoelectric effect

Question

When a certain metallic surface is illuminated with monochromatic light of wavelength $λ$ the stopping potential for photoelectric current is 3V₀ and when the same surface is illuminated with light of wavelength 2 $λ$ , the stopping potential is V₀.The threshold wavelength of this surface for photoelectric effect is

Moderate

A

$6 λ$
B

$4 λ / 3$
C

$4 λ$
D

$8 λ$

Solution

Using photoelectric equation,
$\begin{array}{l} \begin{array}{l} h v - h v_{0} = \frac{1}{2} m v^{2} = e V_{s} \\ or (\frac{h c}{λ} - \frac{h c}{λ_{0}}) = e V_{s} \end{array} \\ For the first case, \frac{h c}{λ} - \frac{h c}{λ_{0}} = e (3 V_{0}) . . . . . . (i) \end{array}$
$\begin{array}{l} For the second case, \frac{h c}{2 λ} - \frac{h c}{λ_{0}} = e (V_{0}) . . . . . . (i i) \\ Solving λ_{0} = 4 λ \end{array}$

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