Cesium Chloride $($CsCl$)$ has a crystal structure that contains $C{s}^{+}$ions in the corner of the cube and a $Cl$ ion at the cube's centre $($see Figure$).$ The $C{s}^{+}$ions are each deficient by one electron, therefore they have a $+$e charge, while $Cl$ ion has one excess electron, and thus they have $-$e charge. If one of the $C{s}^{+}$ions was missing, the crystal is said to have a defect.

What is the magnitude of the net force exerted on the $Cl$ ic the case of a CsCl crystal with a defect $($that is$,$ one $C{s}^{+}$ion is missing$)?$

Useful constants:

$k=8\mathrm{.}988{10}^{9}N{m}^2{C}^{-2}$

$G=6\mathrm{.}674{10}^{-11}{m}^{3}k{g}^{-1}{s}^{-2}$

$e=1\mathrm{.}602{10}^{-19}C$

$m_C=5\mathrm{.}89{10}^{-23}g$

$m_{CS}=2\mathrm{.}21{10}^{-22}g$

In the following questions please show all work and circle your final answer. The first several parts of the question will walk you through a series of steps to reach the final answer.

Find the distance between the $Cl$ ion and any of the $C{s}^{+}$ions assuming that $L=0\mathrm{.}40nm.$