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Question

The maximum kinetic energy of photoelectrons is \( 1.0 \, \text{eV} \) when light of wavelength \( 500
\, \text{nm} \) is used. What is the threshold frequency of the metal? (Take \( h c = 1240 \, \text{eV
nm} \))

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Explanation

**Classical wave theory fails** to explain instant emission, threshold existence, K_max dependence on frequency not intensity, saturation current dependence on intensity. Observations: K_max independent of intensity, exists threshold frequency, emission instantaneous, all explained by photon model E = h f, one photon ejects one electron, energy conservation h f = Φ + K_max. E = (h c/λ) = (1240/500) = 2.48 eV . Φ₀ = E - Kₘₐₓ = 2.48 - 1.0 = 1.48 eV . v₀ = (Φ₀/h) = (1.48 × 1.6 × 10⁻¹⁹/6.63 × 10⁻³⁴) ≈ 3.57 × 10¹⁴ Hz . Applying E = h f = h c/λ, p = h/λ, K_max

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