[د.امير]

What is required is to determine the distance between the centre of a Na+ ion to the centre of the nearest Cl- ion in the NaCl unit cell. To answer the question, please look at the FCC, NaCl unit cell, in the attached figure:

Notice that the length of one side of the unit cell (d) is twice as much as the distance between a Na+ ion and a Cl- ion (x).
d= 2x
Therefore, to find out what d is for NaCl, we need to find the volume of one NaCl unit cell. The volume of the unit cell can be found from the density of NaCl (2.18 g/cm3), which can be applied to any solid no matter how small your "sample" is, even if it is one unit cell, the following expression which we know very well is still valid:
volume = mass/density
Only we need to calculate the mass of NaCl unit cell.
Remember that there are four Na+ and four Cl- ions per unit cell. Let's use those atomic masses given in the question to start out with, then use Avogadro's number to determine the actual mass of four Na+1 and four Cl-1 ions.

4 x 35.5 g/mol = 142 g Cl/mol of unit cells
4 x 23 g/mol = 92 g Na/mol of unit cells

142 + 92 = 234 g/mol of unit cells

Therefore the mass of one unit cell = (234 g NaCl /1mol unit cells) x (1 mol unit cells/6.022x1023 atoms/unit cells) = 3.88 x 10-22 g/unit cell
volume = mass/density
volume = 3.88 x 10-22 g/2.18 g/cm3 = 1.79 x 10-22 cm3
Volume = d^3, or
(d) is the cubed root of 1.79 x 10-22 cm3 = 5.63 x 10-8 cm, the length of one side of the unit cell.
x= d/2 = 5.63 x 10-8 cm/2 = 2.81 x 10-8 cm = 0.281 nm, the distance between a Na+ and a Cl- ions n the unit cell