Question

How many lithium atoms are present in a cubic unit cell with edge length $3.5\, \mathring{A}$ and density $0.53\, gcm ^{-3}$ ?
(Atomic mass of $L i=6.94$ )?

• A. 2
• B. 1
• C. 4
• D. 6

Answer 1

Answer: (A)

$d =\frac{ Z \times M }{ N _{ A } \times a ^{3}}$

$\Rightarrow Z =\frac{ a ^{3} \times d \times N _{ A }}{ M }$

$Z=\frac{\left(3.5 \times 10^{-8}\right)^{3} \times 0.53 \times 6.023 \times 10^{23}}{6.94}$

$= 1.97002 \approx 2$