(Solved): Derive the equation of the Bohr electron velocity using the following relationships: \( \frac{m_{\ ...

Derive the equation of the Bohr electron velocity using the following relationships:

\( \frac{m_{\mathrm{e}} v^{2}}{r_{n}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{r_{n}^{2}} \) \( L=m_{\mathrm{e}} v_{n} r_{n}=m_{\mathrm{e}} \omega_{n} r_{n}^{2}=n \hbar \) \( r_{n}=\frac{4 \pi \varepsilon_{0}}{e^{2}} \frac{(\hbar c)^{2}}{m_{\mathrm{e}} c^{2}}\left(\frac{n^{2}}{Z}\right)=a_{0}\left(\frac{n^{2}}{Z}\right)=(0.5292 \AA) \times\left(\frac{n^{2}}{Z}\right) \)