Question

A metallic element has a simple cubic lattice. Each edge of the unit cell is $2A^o$. The density of the metal is 2.5 g/cc. The number of atoms in the unit cell in $200$ g of the metal is:

• A. $1\times {10}^{25}$
• B. $1\times {10}^{24}$
• C. $1\times {10}^{22}$
• D. $1\times {10}^{20}$

Answer 1

The correct option is A $1\times {10}^{25}$

The formula for density is given below:

$d=\frac{ZM}{N_A{a}^3}=\frac{1\times M}{{6\times 10}^{23}\times {(2\times {10}^{-8})}^3}=2.5$ g/cc
$⟹M=12$ g/mol

Number of moles of element $=\frac{200}{12}=16.7$

Number of atoms $=N_A\times 16.7=1\times {10}^{25}$, where $N_A$ is the Avogadro's number.