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Q.
If $a$ is the radius of first Bohr orbit in a hydrogen atom, the radius of the third orbit is
NTA AbhyasNTA Abhyas 2020Atoms
Solution:
Radius of Bohr orbit is given by
$r_n=\left(\frac{\varepsilon_0 h^2}{\pi m e^2}\right) n^2$
The quantities in the bracket are constant
$\therefore \, \, \, r_{n} \propto n^{2}$
The expression gives the radius of the nth Bohr orbit
$ \, \, \frac{r_{1}}{r_{2}}= \, \frac{n_{1}^{2}}{n_{2}^{2}}$
$ \, \, \frac{a}{r_{2}}= \, \frac{1}{3^{2}}$
$ \, \, r_{2}= \, 9a$