The edge length of unit cell of a metal having molecular weight $75~g/mol$ is $5~ ext{\AA}$ which c

Question

The edge length of unit cell of a metal having molecular weight $75~g/mol$ is $5~	ext{\AA}$ which crystallises in cubic lattice. If the density is $2~g/cc$ then find the radius of metal atom in pm. ($N_{A}=6	imes 10^{23}$)

Professor PC Thomas Classes · Answer

Density $ho = \frac{Z 	imes M}{N_A 	imes a^3} \Rightarrow 2 = \frac{Z 	imes 75}{6 	imes 10^{23} 	imes (5 	imes 10^{-8})^3}$. Solving yields $Z = 2$ (bcc lattice). For bcc, $r = \frac{\sqrt{3}a}{4} = \frac{\sqrt{3} 	imes 5}{4} = 2.165~	ext{\AA} = 216.5~pm$.