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If the wavelength of the incident radiation changes from λ₁ to λ₂ , then the maximum kinetic energy of the emitted photo electrons changes from K₁ to K₂, then the work function of the emitter surface is

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$frac{{{lambda _1}{K_1} - {lambda _2}{K_2}}}{{{lambda _2} - {lambda _1}}}$

$frac{{{lambda _1}{K_2} - {lambda _2}{K_1}}}{{{lambda _1} - {lambda _2}}}$

$frac{{{K_2} - {K_1}}}{{{lambda _1}{K_1} - {lambda _2}{K_2}}}$

$frac{{{lambda _2} - {lambda _1}}}{{{lambda _2}{K_1} - {lambda _1}{K_2}}}$

answer is A.

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Detailed Solution

$E = {W_0} + K{E_{max ;}}$

$therefore frac{{hc}}{lambda } = {W_o} + K{E_{max }}$

$therefore hc = lambda {W_o} + Klambda$

$therefore lambda {W_o} + Klambda = constan t.$

$therefore {lambda _1}{W_o} + {K_1}{lambda _1} = {lambda _2}{W_o} + {K_2}{lambda _2}$

$therefore {W_o} = frac{{{lambda _1}{K_1} - {lambda _2}{K_2}}}{{{lambda _2} - {lambda _1}}}$

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