Question

Two electrons move around a nucleus in circular path of radiur r and 2r.then ratio of their frequencies is

Answer 1

Answer:

$\frac{\nu_1}{\nu_2}=\sqrt2$

Explanation:

Given:

The radius of the two electrons as 'r' and '2r'

Now,

let the frequencies for the two electron be ' υ₁ ' and ' υ₂ ' for the radius r and 2r respectively.

also,

the relation between the radius and the frequency is given as:

$\nu\propto \frac{1}{\sqrt r}$

therefore,

$\nu_1\propto \frac{1}{\sqrt r}$     .............(1)

and,

$\nu_2\propto \frac{1}{\sqrt2r}$  .................(2)

on dividing 1 by 2 we get

$\frac{\nu_1}{\nu_2}=\frac{\frac{1}{\sqrt r}}{\frac{1}{\sqrt 2r}}$

or

$\frac{\nu_1}{\nu_2}=\sqrt\frac{2r}{r}$

or

$\frac{\nu_1}{\nu_2}=\sqrt2$