Question

the ratio of the velocities of an electron in the first three orbits in hydrogen atoms is

Answer 1

Concept Introduction:-

The displacement of an item in unit time are referred as velocity.

Given Information:-

We have been given that the ratio of the velocities of an electron in the first three orbits.

To Find:-

We have to find that the ratio of the velocities of an electron in the first three orbits in hydrogen atoms is

Solution:-

According to the problem

In hydrogen atom the speed of electron is $\mathrm{v}=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{nh}}$........$(1)$

Where, $e$ is the charge of electron

$\mathrm{n}=1$ as first orbit

Dividing equation $(1)$ by $c$

$\frac{\mathrm{v}}{\mathrm{c}}=\frac{\mathrm{e}^{2}}{2 \varepsilon_{0} \mathrm{ch}}$

$\frac{\mathrm{v}}{\mathrm{c}}=\frac{\left(1.6 \times 10^{-19}\right)^{2}}{2 \times 8.85 \times 10^{-12} \times 3 \times 10^{8} \times 6.6 \times 10^{-34}}$

$\frac{\mathrm{v}}{\mathrm{c}}=\frac{1}{137}$

Ratio is $1: 137$

Final Answer:-

The first three orbits in hydrogen atoms is  $1: 137$.

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