Question

At room temperature, sodium crystallises in body-centred cubic lattice with $a=4.24\stackrel{\circ }{A}$.

Calculate the theoretical density of sodium. (Atomic mass of $Na=23.0$)

• A. $1.002gc{m}^{-3}$
• B. $2.002gc{m}^{-3}$
• C. $3.002gc{m}^{-3}$
• D. $None$

Answer 1

Answer: (A)

$1.002gc{m}^{-3}$

$a=4.24\mathring{A};M_{N_A}=23;Z_{eff}\left(BCC\right)=\frac{1}{8}\times 8+1=2$

Density $=\rho =\frac{Z\times N_A}{N_A\times a^3}=\frac{2\times 23}{6.02\times {10}^{23}\times 76.2\times {10}^{-24}}$

$=\frac{460}{76.2\times 6}=1.002gc{m}^{-3}$