Question

An element has a FCC structure with edge length 200 pm. Calculate density if 200 g of this element contains $24\times {10}^{23}$ atoms.

• A. $4.16gc{m}^{-3}$
• B. $41.6gc{m}^{-3}$
• C. $4.16kgc{m}^{-3}$
• D. $41.6kg{m}^{-3}$

Answer 1

The correct option is B $41.6gc{m}^{-3}$

A fcc unit cell contains 4 atoms per unit cell.

Mass of unit cell is equal to mass of 4 atoms. It is equal to $4\times \frac{200}{24\times {10}^{23}}=3.33\times {10}^{-22}$ g

Volume of the unit cell $=(200\times {10}^{-10}{)}^3=8\times {10}^{-24}c{m}^3$

$Density=\frac{Mass}{Volume}=\frac{3.33\times {10}^{-22}}{8\times {10}^{-24}}=41.6g/c{m}^3$