Question

Polonium crystallizes in a simple cubic unit cell. It has atomic mass $209$ and density $91.5kg{m}^{-3}$. What is the edge length of its unit cell?

Answer 1

$\rho =91.5$ $kg/m^3=0.0915$ $g/c{m}^3$

$M_A=209$ $Z=1$ (simple cubic)

$\rho =\frac{Z\times M_A}{N_A\times a^3}\Rightarrow 0.0915=\frac{1\times 209}{6.023\times {10}^{23}\times a^3}$

$a^3=3792.38\times {10}^{-24}$ $c{m}^3$

$\Rightarrow a=15.6\times {10}^{-8}$ $cm=15.6\mathring{A}$