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Question

The maximum kinetic energy of photoelectrons is \( 2.5 \times 10^{-19} \, \text{J} \). What is the
stopping potential? (Take \( e = 1.6 \times 10^{-19} \, \text{C} \))

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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. Kₘₐₓ = e V₀ . V₀ = (Kₘₐₓ/e) = (2.5 × 10⁻¹⁹/1.6 × 10⁻¹⁹) ≈ 1.5625 V . Applying E = h f = h c/λ, p = h/λ, K_max = h f - Φ, Φ = h f₀ = h c/λ₀, λ = h/√(2 m e V) and f_max = e

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