In hydrogen atom, if V n and V p are orbital velocities in n th and p th orbit respectively, then the ratio V p : V n is

Question

In hydrogen atom, if V n ​ and V p ​ are orbital velocities in n th and p th orbit respectively, then the ratio V p ​ : V n ​ is

TestHub · Accepted Answer

The orbital velocity of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $V \propto \frac{1}{n}$ .

For the $n^{th}$ orbit, $V_{n} \propto \frac{1}{n}$ .

For the $p^{th}$ orbit, $V_{p} \propto \frac{1}{p}$ .

Taking the ratio of the two velocities, we get:

$\frac{V _{p}}{V _{n}} = \frac{\frac{1}{p}}{\frac{1}{n}} = \frac{n}{p}$

Thus, $V_{p} : V_{n} = n : p$ .

Answer: $n : p$

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