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The kinetic energies of photoelectrons emitted from a metal are k₁ and k₂ when it is irradiated with light of wavelengths λ₁ and λ₂ respectively. The work function of the metal is ______.

Asked in GUJCET 2013 · Work function and the photoelectric equation

• (1) (k₁λ₂+k₂λ₁)/(λ₂+λ₁)
• (2) (k₁λ₁+k₂λ₂)/(λ₂+λ₁)
• (3) (k₁λ₂-k₂λ₁)/(λ₂-λ₁)
• (4) (k₁λ₁-k₂λ₂)/(λ₂-λ₁)

Step-by-step solution

Why the other options are wrong

• (1) No single slip in the elimination gives this. Test it: with φ₀ = 2 eV, λ₁ = 248 nm gives k₁ = 3 eV and λ₂ = 310 nm gives k₂ = 2 eV; this expression returns 2.56 eV, not 2 eV.
• (2) This is a wavelength-weighted average of k₁ and k₂, a kinetic energy, not the work function. The same test (φ₀ = 2 eV; k₁ = 3 eV at 248 nm, k₂ = 2 eV at 310 nm) returns 2.44 eV.
• (3) Pairs each kinetic energy with the other light's wavelength (k₁ with λ₂); no single slip produces it. The same test returns 7.0 eV, not 2 eV.

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