In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as F =(e^2)/(4 π ε_0)(1/(r^2)+(β)/(r^3)), where…

In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as $\displaystyle \mathrm{F}=\frac{\mathrm{e}^2}{4 \pi \epsilon_0}\left(\frac{1}{\mathrm{r}^2}+\frac{\beta}{\mathrm{r}^3}\right)$, where $\displaystyle \beta$ is a constant. For this atom, the radius of the $\displaystyle \mathrm{n}^{\text {th }}$ orbit in terms of the Bohr radius $\displaystyle \left(\mathrm{a}_0=\frac{\epsilon_0 \mathrm{~h}^2}{\mathrm{~m} \pi \mathrm{e}^2}\right)$ is: