First slide

Photo Electric Effect

Question

A photoelectric surface is illuminated successively by monochromatic light of wavelength $λ and \frac{λ}{2} .$ If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the material is
(h = Planck's constant, c = speed of light)

Moderate

A

$\frac{2 hc}{λ}$
B

$\frac{hc}{3 λ}$
C

$\frac{hc}{2 λ}$
D

$\frac{hc}{λ}$

Solution

Let $ϕ_{0}$ be the work function of the surface of the material. Then,
According to Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectrons in the first case is
$K_{\max_{1}} = \frac{h c}{λ} - ϕ_{0}$
and that in the second case is
$K_{\max_{2}} = \frac{h c}{\frac{λ}{2}} - ϕ_{0} = \frac{2 h c}{λ} - ϕ_{0}$
$But K_{\max_{2}} = 3 K_{\max_{1}} (given)$
$∴ \frac{2 h c}{λ} - ϕ_{0} = 3 (\frac{h c}{λ} - ϕ_{0})$
$\frac{2 h c}{λ} - ϕ_{0} = \frac{3 h c}{λ} - 3 ϕ_{0}$
$3 ϕ_{0} - ϕ_{0} = \frac{3 h c}{λ} - \frac{2 h c}{λ}$
$2 ϕ_{0} = \frac{h c}{λ} or ϕ_{0} = \frac{h c}{2 λ}$

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