Question

You have one electron directly over another electron. The force between the electrons is a repulsiveforce of 9.11 x 10-30 Newtons. If the charge of each electron is 1.6 x 10-19 Coulombs, what is the distancebetween the electrons?

Answer 1

Given:

The force of repulsion between the electrons is,

`F=9.11*10^(-30)\text{ N}`

The charge of each electron is,

`e=1.6*10^(-19)\text{ C}`

To find:

The distance between the electrons

Step-by-step explanation:

The force between two electrons at a distance 'r' is,

`\begin{gathered} F=(e^2)/(4\pi\in_0r^2) \\ Here,\text{ }(1)/(4\pi\in_0)=9*10^9\text{ N.m}^2.C^(-2) \end{gathered}`

Substituting the values, we get,

`\begin{gathered} 9.11*10^(-30)=9*10^9*((1.6*10^(-19))^2)/(r^2) \\ r^2=((1.6*10^(-19))^2*9*10^9)/(9.11*10^(-30)) \\ r^2=25.29 \\ r=5.03\text{ m} \end{gathered}`

Hence, the distance between the electrons is 5.03 m.