First slide

Photoelectric effect and study of photoelectric effect

Question

Light of wavelength $λ$ strikes a photoelectric surface and electrons are ejected with kinetic energy K. If K is to be increased to exactly twice its original value, the
wavelength must be changed to $λ$ ' such that

Difficult

A

$λ^{'} < λ / 2$
B

$λ^{'} > λ / 2$
C

$λ > λ^{'} > λ / 2$
D

$λ^{'} = λ / 2$

Solution

Case 1: $\frac{h c}{λ} = E + ϕ_{0}$
Case 2 : $\frac{h c}{λ^{'}} = 2 E + ϕ_{0}$
$Dividing, we get \frac{λ^{'}}{λ} = (\frac{E + ϕ_{0}}{2 E + ϕ_{0}}) or \frac{λ^{'}}{λ} < 1$
$∴ λ^{'} < λ or λ > λ^{'} . . . . . . . . . . . . (i)$
$\begin{array}{l} Also, \frac{λ^{'}}{λ} = \frac{1}{2} [\frac{E + ϕ_{0}}{E + \frac{ϕ_{0}}{2}}] \\ or \frac{λ^{'}}{λ} > \frac{1}{2} or λ^{'} > \frac{λ}{2} . . . . . . . . . . . (i i) \end{array}$
It follows from Eqs. (i) and (ii) we can conclude that $λ > λ^{'} > \frac{λ}{2}$

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