Question

How much work must be done to bring three electrons from a great distance apart to 2.5×10−10 m from one another (at the corners of an equilateral triangle)?

Answer 1

Answer:

Explanation:

Given

Distance between two electrons arranged in equilateral triangle geometry is

$a=2.5\times 10^{-10}\ m$

Potential Energy Between two system

$U=\frac{kq_1q_2}{r}$

where $q_1$ and $q_2$ are charges and r is the distance between them

For three Charges Potential Energy is given by

$U=k\left ( \frac{q_1q_2}{r_{12}}+\frac{q_2q_3}{r_{23}}+\frac{q_1q_3}{r_{13}}\right )$

$q_1=q_2=q_3=1.6\times 10^{-19}\ C$

$r_{12}=r_{23}=r_{13}$

$U=3\times \left ( \frac{9\times 10^9\cdot (1.6\times 10^{-19})^2}{(2.5\times 10^{-10})}\right )$

$=27.648\times 10^{-19}\ J$