Question

Copper crystallises with face centered unit cell. if the radius of the copper atom is $127.8pm$. calculate the density of the copper metal $(atomicmassofCu=63.55u)$.

Answer 1

Number of atoms in unit cell, $Z=4$

Radius $r=127.8pm$

For Face center cubic $r=\frac{a}{2\sqrt{2}}$

$127.8\times 2\sqrt{2}=a$

$a=361.42pm$

$a=361.41\times {10}^{-10}cm$

Atomic mass of cell $=63.55g/mol$

Density $=\frac{Z\times M}{a^3\times N_A}$

$=\frac{4\times 63.55}{361.41\times {10}^{-10}\times 6.022\times {10}^{23}}$

$=8.9\times {10}^{-14}g/c{m}^3$