Physics - Modern Physics Question with Solution | TestHub

Concept: Bohr orbit radius The electron undergoes a uniform circular motion in Bohr's orbit. The coulombic attraction of the nucleus balancing the centrifugal force: $\frac{{\mathrm{mv}}^2}{\mathrm{r}}=\frac{\mathrm{eZ}}{4\pi {\epsilon }_0{\mathrm{r}}^2}$ Further, the angular momentum of electron in Bohr's orbit is: $\mathrm{mvr}=\frac{\mathrm{nh}}{2\pi }$ On squaring the second equation and dividing it by the first equation: $r\propto \frac{n^2}{Z}$ The smallest Bohr orbit has radius ${\mathrm{a}}_0$ as $\mathrm{n}=1$. Using the above functional dependence of the Bohr orbit, the third orbit is has radius $9{\mathrm{a}}_0$.