Problem: You may want to reference (Pages 165 - 166) Section 5.1 while completing this problem.A magnesium ion, Mg2+, with a charge of 3.2x10-19 C and an oxide ion, O2-, with a charge of -3.2x10-19 C, are separated by a distance of  0.40 nm.  How much work would be required to increase the separation of the two ions to an infinite distance?

FREE Expert Solution

E → electrostatic potential energy

$\boxed{\mathbf{W}\mathbf{=}{\mathbf{E}}_{\mathbf{final}}\mathbf{-}{\mathbf{E}}_{\mathbf{initial}}}$

$\boxed{\mathbf{E}\mathbf{=}{\mathbf{k}}_{\mathbf{e}}\frac{{\mathbf{Q}}_{\mathbf{1}}\mathbf{·}{\mathbf{Q}}_{\mathbf{2}}}{\mathbf{d}}}$

Initially, distance of  0.40 nm:

1 nm = 10^-9 m

$\mathbf{d}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{ }\cancel{\mathbf{nm}}\mathbf{\times }\frac{{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{ }\mathbf{m}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{nm}}}$

d = 4.0x10^-10 m