Question

The density of lead is $12.40$ g$/c{m}^3$ and the metal crystallizes with fcc unit cell estimate the radius of lead atom?

Answer 1

$\rho =12.4$ $g/c{m}^3$

$Z=4$ (for FCC)

$M_A=207.2$

$a=?$

$N_A=6.023\times {10}^{23}$

$\rho =\frac{Z\times M_A}{N_A\times a^3}$

$\Rightarrow 12.4=\frac{4\times 207.2}{6.023\times {10}^{23}}$

$\Rightarrow a^3=110.9\times {10}^{-24}$ $c{m}^3$

$\Rightarrow a=4.8\times {10}^{-8}$ $cm$

$\Rightarrow a=4.8\mathring{A}$

In FCC unit cell $4r=a\sqrt{(}2)$ (along face diagonal)

$r=\frac{4.8}{2\sqrt{2}}=1.69\mathring{A}$