Chemistry - Atomic Structure Question with Solution | TestHub

The energy of an electron in the ${\mathrm{n}}^{\mathrm{th}}$ Bohr orbit of a hydrogen atom can be calculated using the formula:

$$\begin{gathered} {\mathrm{E}}_{\mathrm{n}}=\frac{-2.18\times {10}^{-18}{\mathrm{Z}}^2}{{\mathrm{n}}^2} \\ \mathrm{Where} \mathrm{n} \mathrm{is} \mathrm{the} \mathrm{principal} \mathrm{quantum} \mathrm{number} \mathrm{of} \mathrm{the} \mathrm{Bohr} \mathrm{orbit}. \\ {\mathrm{E}}_{\mathrm{n}}\mathrm{\alpha }\frac{1}{{\mathrm{n}}^2} \\ {\mathrm{E}}_{\mathrm{n}}\mathrm{\alpha }\frac{1}{9} \end{gathered}$$

Therefore, the energy of the electron in the third Bohr orbit of a hydrogen atom is Three times of this value.