Discussion
A pair of \(Li^{+}\) and \(Cl^{-}\) ions, with their radii 0.60 Å and 1.81 Å respectively, touch each other. The attractive force between them is :
Answer: C
The attractive force is about \(3.96 \times 10^{-9}\) N.
The ions touch, so the distance between their centres is the sum of the radii, 0.60 + 1.81 = 2.41 Å. Each carries one electronic charge:
\[ \begin{aligned} F &= \frac{e^{2}}{4\pi\varepsilon_{0}r^{2}} \\ &= \frac{(9 \times 10^{9})(1.6 \times 10^{-19})^{2}}{(2.41 \times 10^{-10})^{2}} \\ &= \frac{2.30 \times 10^{-28}}{5.81 \times 10^{-20}} = 3.96 \times 10^{-9}\ \text{N} \end{aligned} \]
Using a single radius, or the difference of the radii, instead of their sum gives a very different value; the other options do not correspond to the correct separation.
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