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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

Work Function from Photoelectric Data

Work Function Calculation

If kinetic energy of photoelectrons changes from K₁ to K₂ as wavelength changes from λ₁ to λ₂:

Work function (φ) is: φ = (h c / λ₁) - K₁ = (h c / λ₂) - K₂

Or rearranged: φ = [K₁ λ₂ - K₂ λ₁] / [λ₂ - λ₁] (where h and c included for full units)

Variables

h: Planck's constant
c: Speed of light
λ: Wavelength of incident light
K: Maximum kinetic energy of photoelectrons

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