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 $=6.2gc{m}^{-3}$ )

• 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 $=AB=2r$

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 $=\frac{23}{6.023\times 10^{23}\times 6.20}$
$\frac{4}{3}\pi r^3=\frac{23}{6.02\times 10^{23}\times 6.2}$
$r^3=\frac{3\times 23}{4\pi \times 6.02\times 10^{23}\times 6.2}$
$r^3=1.47\times 10^{-24}c{m}^3$
$r=1.137\times 10^{-8}cm$
$2r=2.274\times 10^{-8}cm=2.274\mathring{A}$