Question

An element crystallizes in a structure having fcc unit cell of an edge length of $200pm$. Calculate the density (in $gc{m}^{-3}$), if $200g$ of this element contains $24\times {10}^{23}$ atoms.

• A. 41.6
• B. 83.3
• C. 119.4
• D. 28.9

Answer 1

The correct option is A 41.6

Given,
$200g$ of element contains $24\times {10}^{23}$
Thus,
$\text{Molar mass of element, M}=\frac{N_A\times 200}{24\times {10}^{23}}=50.2g$
For fcc,
$\text{Number of elements in an unit cell, Z}=4$

$\text{Density of unit cell,}\rho =\frac{ZM}{N_A\times V}$
Where,
V is the volume of unit cell.
$\text{Edge length of unit cell, a}=200pm=200\times {10}^{-10}cm$
$\text{Volume of unit cell, V}=a^3=(200\times {10}^{-10}{)}^3$

$\rho =\frac{4\times 50.2}{6.023\times {10}^{23}\times (200\times {10}^{-10}{)}^3}$
$\rho =\frac{200.8}{6.023\times 8\times {10}^{-1}}$

$\rho =41.67gc{m}^{-3}$