Question

Find the ratio of the time period of revolution of electron in $He ^{+}$ion sample in the orbit where the path length is $3$ times the de Broglie wavelength to the time period of revolution in the ground state.

Answer 1

$2 \pi r=3 \lambda$
$\Rightarrow \frac{2 \pi r}{\lambda}=3$
$\Rightarrow n=3$
$\therefore \frac{T_{1}}{T_{2}}=\frac{n_{1}^{3}}{n_{2}^{3}}$
$=\frac{3^{3}}{1^{3}}=27$