Question

Lead metal has a density of $11.34$ g cm${}^{-3}$ and crystallizes in a face-centered lattice. Choose the correct alternatives.

• A. The volume of one unit cell is $1.214\times {10}^{-22}$ cm${}^3$
• B. The volume of one unit cell is $1.214\times {10}^{-19}$ cm${}^3$
• C. The atomic radius of lead is $175$ pm
• D. The atomic radius of lead is $155.1$ pm

Answer 1

Answer: (A), (C)

The atomic radius of lead is $175$ pm
The volume of one unit cell is $1.214\times {10}^{-22}$ cm${}^3$

The expression for density is given below:

$\text{Density}=\frac{Z\times M}{N_A\times \text{volume}}$

$\text{Volume}=\frac{4\times 207}{6.02\times {10}^{23}\times 11.34}=1.213\times {10}^{-22}$ cm${}^3$

For FCC, we have $4r=a\sqrt{2}$

$r=\frac{4.95\times {10}^{-8}\times \sqrt{2}}{4}=175$ pm

$\text{Volume}=a^3=1.213\times {10}^{-22}$ cm${}^3$

$\text{Edge length}=a={\left(1.213{10}^{-24}\right)}^{\frac{1}{3}}$ $⟹a=4.95\times$ ${10}^{-8}$ cm