If the wavelength of the incident radiation changes from $λ_{1}$ to $λ_{2}$ , then the maximum kinetic energy of the emitted photoelectrons changes from $k_{1}$ to $k_{2}$ . The work function of the emitter surface is

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

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

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

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

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{h c}{λ_{1}} = w + k_{1} - - - - (1) \\ \frac{h c}{λ_{2}} = w + k_{2} - - - - - (2) \\ \frac{λ_{2}}{λ_{1}} = \frac{w + k_{1}}{w + k_{2}} \\ w = \frac{k_{1} λ_{1} - k_{2} λ_{2}}{λ_{2} - λ_{1}} \end{array}$

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