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Question

What is the wavelength of the photon emitted when an electron drops from \( n = 2 \) to \( n = 1 \) in
a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \), \( c = 3 \times 10^8 \, \text{m/s}
\), 1 eV = \( 1.6 \times 10^{-19} \, \text{J} \))

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Explanation

**Bohr's stationary orbits** defined by angular momentum quantization L = n ħ, ħ = h/2π, n=1 ground state, electron in these orbits does not radiate despite acceleration, contrary to classical EM theory which predicts atom collapse due to energy loss via radiation, Bohr postulates to explain observed stability and discrete spectra. Δ E = 10.2 eV = 1.632 × 10⁻¹⁸ J . λ = (hc/Δ E) = (6.6 × 10⁻³⁴ × 3 × 10⁸/1.632 × 10⁻¹⁸) ≈ 1.21 × 10⁻⁷ m . 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

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