Question

Calculate the velocity of the electron in the first Bohr orbit of the hydrogen atom (Given, r = a)

Answer 1

Step 1: Given data

$\mathrm{n}=1$;

$\mathrm{h}=6.626\times {10}^{-34}\mathrm{Js}$

$\mathrm{m}=9.1\times {10}^{-31}\mathrm{kg}$

Step 2: Introducing the formula for calculating the velocity of an electron:

$\mathrm{mvr}=\frac{\mathrm{nh}}{2\mathrm{\pi }}$

Step: 3 Putting all the values in the above-mentioned equation

$$\begin{gathered} \mathrm{v}=\frac{\mathrm{nh}}{2\mathrm{\pi mr}} \\ \mathrm{v}=\frac{1\times 6.626\times {10}^{-34}}{2\times 3.14\times 9.1\times {10}^{-31}\times 0.529\times {10}^{-10}}{\mathrm{ms}}^{-1} \\ \mathrm{v}=\frac{6.626\times {10}^{-34}}{30.23\times {10}^{-41}}{\mathrm{ms}}^{-1}=\frac{6.626\times {10}^7}{30.23}{\mathrm{ms}}^{-1}=0.219\times {10}^7{\mathrm{ms}}^{-1} \\ \mathrm{v}=2.19\times {10}^6{\mathrm{ms}}^{-1} \end{gathered}$$

Therefore, the velocity of the electron in the first Bohr orbit of the hydrogen atom is $2.19\times {10}^6{\mathrm{ms}}^{-1}$.