Question

An element crystallizes as a face-centred cubic lattice with edge length equal to $460$ pm. The density (in gcm${}^{-3}$) of the element X when molar mass of X atom is $60$ gmol${}^{-1}$ is:

• A. $4.096$
• B. $2.048$
• C. $6.144$
• D. $3.072$

Answer 1

The correct option is A $4.096$

The formula for calculating density is given below:

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

where,

$d=$ density of the unit cell

$z=$ effective number of atoms in the fcc unit cell $=4$

$M=$ molar mass $=60g/mol$

$N_A=$ Avogadro number

$a^3=$ volume of the unit cell $=(460\times {10}^{-10}{)}^{3}c{m}^3$

Substituting the value, we get

$d=\frac{z\times M}{N_A\times a^3}$ $=\frac{4\times 60}{{6.023\times 10}^{23}\times {(460\times {10}^{-10})}^3}=4.096$ g cm${}^{-3}$