Question

Atoms of the element $X$ are spherical. Each atom of the element (atomic mass $23$ ) is at the corner of the cube and is in contact along the edge length, then edge length is (density $=6.2 \,g \,cm ^{-3}$ )

• A. $2.274 \mathring{A}$
• B. $1.137 \mathring{A}$
• C. $4.548 \mathring{A}$
• D. $1.183 \mathring{A}$

Answer 1

Answer: (A)

Edge length $=A B=2 r$

Volume of the spherical atom $=\frac{4}{3} \pi r^3$
$\frac{\text { Mass }}{\text { Volume }}=$ density
Volume $=\frac{\text { mass }}{\text { density }}$
Mass of one atom $=\frac{m}{N_0}=\frac{23}{6.02 \times 10^{23}}$
$\therefore$ Volume $=\frac{23}{6.023 \times 10^{23} \times 6.20}$
$\frac{4}{3} \pi r^3=\frac{23}{6.02 \times 10^{23} \times 6.2}$
$r^3=\frac{3 \times 23}{4 \pi \times 6.02 \times 10^{23} \times 6.2}$
$r^3=1.47 \times 10^{-24} cm ^3$
$r=1.137 \times 10^{-8} cm$
$2 r=2.274 \times 10^{-8} cm =2.274 \mathring{A}$