Question

An element of density $7gc{m}^{-3}$ occurs in bcc structure with cell edge of $300pm$. Calculate the number of atoms present in $200g$ of the element.

• A. $$1.2\times {10}^{24}$$
• B. $$1.2\times {10}^{42}$$
• C. $$2.1\times {10}^{24}$$
• D. $$2.4\times {10}^{42}$$

Answer 1

The correct option is C $$2.1\times {10}^{24}$$

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$$\text{Mass of unit cell}=\text{density}\times \text{volume of unit cell}$
$=7gc{m}^{-3}\times (3\times {10}^{-8}cm{)}^3$
$=189\times {10}^{-24}g$
$\text{No. of atom in bcc structure}=2$
$\text{Mass of atom}=\frac{\text{Mass of unit cell}}{2}$
$=\frac{189\times {10}^{-24}g}{2}$
$\text{Mass of atom}=94.5\times {10}^{-24}g$

$\text{No. of atoms}=\frac{200g}{94.5\times {10}^{-24}g}$
$\text{No. of atoms}=2.11\times {10}^{24}\text{atoms}$