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Question

The radius of the first orbit in a hydrogen atom is \( 5.3 \times 10^{-11} \, \text{m} \). What is the
radius of the second orbit?

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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. Radius r_n = n² r₁ , where r₁ = 5.3 × 10⁻¹¹ m . For n = 2 : r₂ = 2² × 5.3 × 10⁻¹¹ = 4 × 5.3 × 10⁻¹¹ = 2.12 × 10⁻¹⁰ m . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀

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