Question

A metalic elemet has a simple cubic lattice. Each edge of the unit cell is $2\stackrel{\circ }{A}$. The density of the metal is $2.5g/cc$. The number of atoms in $200g$ 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:
$d=\frac{ZM}{N_A{a}^3}=\frac{1\times M}{6\times {10}^{23}\times (2\times {10}^{-8}{)}^3}=2.5g/cc$
$\Rightarrow M=12g/mol$
Number of moles of element $\Rightarrow \frac{200}{12}=16.7$
Number of atoms $=N_A\times 16.7\approx 1\times {10}^{25},$ where $N_A$ is the Avogadro's number.