First slide

Photo Electric Effect

Question

If the wavelength of the incident radiation changes from $λ_{1} t o λ_{2}$ , then the maximum kinetic energy of the emitted photo electrons changes from $K_{1} t o K_{2}$ ,then the work function of the emitter surface is

Moderate

A

$\frac{λ_{1} K_{1} - λ_{2} K_{2}}{λ_{2} - λ_{1}}$
B

$\frac{λ_{1} K_{2} - λ_{2} K_{1}}{λ_{1} - λ_{2}}$
C

$\frac{K_{2} - K_{1}}{λ_{1} K_{1} - λ_{2} K_{2}}$
D

$\frac{λ_{2} - λ_{1}}{λ_{2} K_{1} - λ_{1} K_{2}}$

Solution

$\frac{h c}{λ_{1}} = W + K_{1}$
dividing both
$\frac{h c}{λ_{2}} = W + K_{2}$
$\frac{λ_{2}}{λ_{1}} = \frac{w + k_{1}}{w + k_{2}}$
$λ_{2} w + λ_{2} k_{2} = λ_{1} w + λ_{1} w + λ_{1} k_{1}$
$λ_{2} k_{2} - λ_{1} k_{1} = w (λ_{1} - λ_{2})$
$w = \frac{λ_{2} k_{2} - λ_{1} k_{1}}{λ_{1} - λ_{2}} = \frac{λ_{1} k_{1} - λ_{2} k_{2}}{λ_{2} - λ_{1}}$

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