A photoelectric surface is illuminated successively by monochromatic light of wavelength and . 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 mater

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Solution

Q.
A photoelectric surface is illuminated successively by monochromatic light of wavelength $λ$ and $λ / 2$ . 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) [2015]

1 $\frac{2 h c}{λ}$

2 $\frac{h c}{3 λ}$

3 $\frac{h c}{2 λ}$

4 $\frac{h c}{λ}$

Ans.
(3)

Let $ϕ_{0}$ be the work function of the surface of the material.
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)

$∴$    $\frac{2 h c}{λ} - ϕ_{0} = 3 (\frac{h c}{λ} - ϕ_{0});$    $\frac{2 h c}{λ} - ϕ_{0} = \frac{3 h c}{λ} - 3 ϕ_{0}$

$3 ϕ_{0} - ϕ_{0} = \frac{3 h c}{λ} - \frac{2 h c}{λ} or 2 ϕ_{0} = \frac{h c}{λ} or ϕ_{0} = \frac{h c}{2 λ}$

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