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On the basis of Bohr’s theory, derive an expression for the radius of the nth orbit of an electron…
On the basis of Bohr’s theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
Given: Centripetal electrostatic force $\frac{m v^2}{r} = \frac{1}{4\pi\varepsilon_0} \frac{e^2}{r^2}$ and Bohr's quantization condition $m v r = \frac{n h}{2\pi}$
To show: $r_n = \frac{n^2 h^2 \varepsilon_0}{\pi m e^2}$
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From ISC 2022 Specimen Physics Paper 1, question 10.