Question

A metal crystallizes in FCC structure. Calculate the atomic mass of metal,If the edge length of the unit cell is $404$pm and its density is $2.7gc{m}^{-3}$

Answer 1

Given, cell is FCC, $z=4$

Edge length, $a=404pm=4.04\times {10}^{-8}cm$

Density of metal, $d=2.72g{cm}^{-3}$

$N_A=6.02\times {10}^{23}{mol}^{-1}$

Mass of the metal, $M=?$

We know,

$d=\frac{z\times M}{a^3\times N_A}$

$M=\frac{d\times N_A\times a^3}{z}$

$M=\frac{2.72\times (4.04\times {10}^{-8}{)}^3\times 6.02\times {10}^{23}}{4}$

Mass, $M=27g$ ${mol}^{-1}$