Question

If an electron is revolving around the hydrogen nucleus at a distance of 0.1 nm, what should be its speed

Answer 1

Given that,

Distance at which the electron is revolving is 0.1 nm.

To find,

The speed of the electron.

Solution,

When the electron is revolving, the centripetal force is balanced by the electrostatic force such that,

$\dfrac{1}{4\pi \epsilon_o}\dfrac{Ze^2}{r^2}=\dfrac{mv^2}{r}$

v is speed of electron

m is mass of electron

Z is atomic number of hydrogen

So,

$v=\sqrt{\dfrac{Ze^2}{4\pi \epsilon_o mr}}$

$v=\sqrt{\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{9.1\times 10^{-31}\times 0.1\times 10^{-9}}} \\\\v=1.59\times 10^6\ m/s$

So, the speed of the electron is $1.59\times 10^6\ m/s$.