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Question

A hydrogen atom in the \( n = 5 \) state emits a photon and returns to the ground state. What is the
maximum energy of the photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

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Explanation

**Thomson's plum pudding model** positive charge uniformly distributed in sphere with electrons embedded, positive charge spread, fails to explain large angle scattering observed. Bohr's model introduces stationary orbits with quantized angular momentum L = n h/2π, physical basis de Broglie standing wave condition 2πr = n λ, circumference fits n wavelengths, explains line spectrum. E₅ = -0.544 eV , E₁ = -13.6 eV . Δ E = -0.544 - (-13.6) = 13.056 eV ≈ 13.06 eV . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation

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