An electron in a hydrogen atom is in an orbit from which there can be a maximum of six transitions. Another electron in a different hydrogen atom is in an orbit from which there can be a maximum of th

Question

An electron in a hydrogen atom is in an orbit from which there can be a maximum of six transitions. Another electron in a different hydrogen atom is in an orbit from which there can be a maximum of three transitions. The ratio of the velocities of the electrons in these two orbits is

TestHub · Accepted Answer

Number of spectral lines obtained due to transition of electrons from $n^{t h}$ orbit to lower orbit is,

$N =$ $\frac{n (n - 1)}{2}$

For case - 1, $N = 6 =$ $\frac{n_{1} (n_{1} - 1)}{2}$

$\Rightarrow n_{1} = 4$

For case - 2, $N = 3 =$ $\frac{n_{2} (n_{2} - 1)}{2}$

$\Rightarrow n_{2} = 3$

The velocity of electron in a hydrogen atom in $n$ th orbit

$v_{n} \propto \frac{1}{n}$

$\frac{v_{n}}{{v^{'}}_{n}} = \frac{n_{2}}{n_{1}}$

$\Rightarrow \frac{n_{6}}{n_{3}} = \frac{3}{4}$

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