Question

An element crystallises in a structure having a $fcc$ unit cell of an edge $200pm$. If $200g$ of this element contains $24\times 10^{23}$ atoms then its density is

• A. $41.66gc{m}^{-3}$
• B. $313.9gc{m}^{-3}$
• C. $8.117gc{m}^{-3}$
• D. $400gc{m}^{-3}$

Answer 1

Answer: (A)

Molar mass of the element
$=\frac{200}{24\times 10^{23}}\times 6.023\times 10^{23}$
$=50.19gmo{l}^{-1}$
For $fcc,Z=4$,
$V=a^3={\left(200\times 10^{-10}\right)}^3$
$d=\frac{Z\times M}{N_A\times V}$
$=\frac{4\times 50.19}{6.023\times 10^{23}\times {\left(200\times 10^{-10}\right)}^3}$
$=41.66gc{m}^{-3}$