In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as \[F=\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( \frac{1}{{{r}^{2}}}+\frac{\beta }{{{r}^{3}}} \right),\] where \[\beta \] is a constant. For this atom, the radius of the nth orbit in terms of the Bohr radius \[\left( {{a}_{0}}=\frac{{{\varepsilon }_{0}}{{h}^{2}}}{m\pi {{e}^{2}}} \right)\] is:

• A.  \[{{r}_{n}}={{a}_{0}}n-\beta \]
• B.  \[{{r}_{n}}={{a}_{0}}{{n}^{2}}+\beta \]
• C.  \[{{r}_{n}}={{a}_{0}}{{n}^{2}}-\beta \]
• D.  \[{{r}_{n}}={{a}_{0}}n+\beta \]