Rock salt, NaCl ( $M = 58.5 g mo l^{- 1}$ ), has an fcc arrangement of ions with 4 formula units per unit cell and density $2.165 g c m^{- 3}$ . With $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ , calculate the unit cell edge length in pm (nearest integer).

Numerical answer type, answer in pm, tolerance 1.

Answer: 564 pm

ρ = \frac{ZM}{N _{A} a ^{3}}

gives

a^{3} = \frac{4 \times 58.5}{6.022 \times 1 0 ^{23} \times 2.165} = 1.7948 e - 22 c m^{3}

. Taking the cube root,

a = 5.6408 \times 1 0^{- 7} cm \approx 564 pm