Physics - Current Electricity Question with Solution | TestHub

According to Bohr's theory of hydrogen atom, (i) The speed of the electron in the $n$th orbit $$V_n=\frac{1}{n}\frac{e^2}{4\pi {\epsilon }_0(h/2\pi )}\text{ or }{v}_n\propto \frac{1}{n}$$ (ii) The energy of the electron in the $n$th orbit $$E_n=\frac{m{e}^4}{8n^2{\epsilon }_0^2{h}^2}=\frac{-13.6}{n^2}eV\text{ or }{E}_n\propto \frac{1}{n^2}$$ (iii) The radius of the electron in the $n$th orbit $$r_n=\frac{n^2{h}^2{\epsilon }_0}{\pi m{e}^2}=n^2{a}_0\text{ or }{r}_n\propto n^2$$ where $a_0=\frac{h^2{\epsilon }_0}{\pi me}=5.29\times 10^{-11}\mathrm{m}$