Question

The unit cell of a metallic element of atomic mass 108 and density 10.5 ${g/cm}^3$ is a cube with edge length of 409 pm. The structure of the crystal lattice is:

• A. fcc
• B. bcc
• C. hcp
• D. None of these

Answer 1

The correct option is A fcc

We know that,

Density-

$d=\frac{Z\times M}{a^3\times NA}$

Given :

Molar Mass$\left(M\right)=108g/mol$

Density $\left(d\right)=10.5g/c{m}^3$

Edge Length$\left(a\right)=409pm$

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

Value of $N_A$ is $N_A=6.023\times {10}^{23}$

$Z=\frac{10.5\times (409\times {10}^{-10}c{m}^3{)}^3\times 6.023\times {10}^{23}}{108}=4$

Number of atoms $=4$

Hence the element is packed in FCC structure.