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Question

The work function of a metal is \( 2.2 \, \text{eV} \). What is the threshold wavelength in nm? (Take
\( h c = 1240 \, \text{eV nm} \))

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Explanation

**Photoelectric effect** demonstrates particle nature of light, photon energy E = h f, work function Φ = h f₀ minimum energy to eject electron, threshold frequency f₀ = Φ/h, threshold wavelength λ₀ = hc/Φ, hc=1240 eV·nm, maximum kinetic energy K_max = h f - Φ = e V₀, V₀ stopping potential, photocurrent proportional to intensity (number of photons) when f>f₀, saturation current depends on intensity, frequency determines K_max not current. λ₀ = (h c/Φ₀) = (1240/2.2) ≈ 563.64 nm . Applying E = h f = h c/λ, p = h/λ, K_max = h f - Φ, Φ = h f₀ = h c/λ₀, λ

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