Question

Sodium chloride is an ionic compound; we can effectively model it as being composed of sodium atoms with one electron removed next to chlorine atoms with one electron added. The attractive force between the positive and negative charges holds the crystal together. If you model the sodium and chlorine ions as point charges separated by 0.28 nm, the spacing in the crystal, what is the magnitude of the attractive force between the two ions? How does this compare to the weight of the sodium ion, which has a mass of 23 u?

Answer 1

The magnitude of the attractive force is,

\(F=\frac{k q^{2}}{r^{2}}=\frac{\left(9 \times 10^{9}\right)\left(1.6 \times 10^{-19} \mathrm{C}\right)^{2}}{\left(0.28 \times 10^{-9} \mathrm{~m}\right)^{2}}=2.94 \times 10^{-9} \mathrm{~N}\)

The weight of the sodium is,

\(\begin{aligned} W &=m g \\ &=(23 \mathrm{u})\left(\frac{1.67 \times 10^{-27} \mathrm{~kg}}{1 \mathrm{u}}\right)\left(9.8 \mathrm{~m} / \mathrm{s}^{2}\right) \\ &=3.76 \times 10^{-25} \mathrm{~N} \end{aligned}\)