Answer
0.282 nm.
Work Step by Step
Use the hint. Every ion sits at the corner of a cube of side length s, which is the distance between ions.
See Figure 29–20. A cube of side length s is associated with four NaCl pairs. However, only one-eighth of each Na or Cl ion is part of that cube, because 8 cubes meet at that corner.
In summary, each cube of side length s has the equivalent of one-half of an NaCl molecule.
Calculate the mass per unit volume, i.e., the density.
$$\rho=\frac{0.5m_{NaCl}}{s^3}$$
$$s=\left( \frac{0.5m_{NaCl}}{\rho}\right)^{1/3}$$
$$s=\left( \frac{0.5(58.44 g/mole)}{2.165g/cm^3}\frac{mole}{6.02\times10^{23}}\right)^{1/3}$$
$$s=2.82\times10^{-8}cm$$