Sodium (atomic mass 23) is bcc and has density 0.97 g cm^-3. Using N_A = 6.022x10^23 mol^-1, find the edge length of its unit cell in pm (nearest integer).

JEE Main levelNumerical answerDifficulty 2 of 3ss065

Sodium (atomic mass 23) is bcc and has density $0.97 g c m^{- 3}$ . Using $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ , find the edge length of its unit cell in pm (nearest integer).

Numerical answer type, answer in pm, tolerance 1.

a^{3} = \frac{ZM}{N _{A} ρ} = \frac{2 \times 23}{6.022 \times 1 0 ^{23} \times 0.97} = 7.87 \times 1 0^{- 23} c m^{3}

, so

a = 428.6 pm \approx 429 pm