An element crystallises in a bcc lattice with cell edge of \(500 \mathrm{pm}\). The density of the element is \(7.5 \mathrm{~g} \mathrm{~cm}^{-3}\). How many atoms are present in \(300 \mathrm{~g}\) of metal ?

(B)
\(a=500 \mathrm{pm}=5 \times 10^{-8} \mathrm{~cm}\)
\(\therefore \mathrm{a}^{3}=\left(5 \times 10^{-8} \mathrm{~cm}\right)^{3}=125 \times 10^{-24} \mathrm{~cm}^{3}\)
\(\rho=7.5 \mathrm{~g} \mathrm{~cm}^{-3}, \mathrm{~m}=300 \mathrm{~g}, \mathrm{n}=2(\) for bcc cell \()\)
\(\rho=\frac{\mathrm{nM}}{\mathrm{a}^{3} \mathrm{~N}_{\mathrm{A}}} \quad \therefore \mathrm{M}=\frac{\rho \times \mathrm{a}^{3} \times \mathrm{N}_{\mathrm{A}}}{\mathrm{n}}\)
\(\therefore M=\frac{7.5 \times 125 \times 10^{-24} \times 6.022 \times 10^{23}}{2}=282.3 \mathrm{~g} \mathrm{~mol}^{-1}\)
\(282.3 \mathrm{~g}\) of metal contains \(6.022 \times 10^{23}\) atoms
\(\therefore 300 \mathrm{~g}\) of metal contains \(\frac{6.022 \times 10^{23} \times 300}{282.3}=6.399 \times 10^{23}\) atoms \(\approx 6.4 \times 10^{23}\) atoms