Question

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\mathring{A}.\, 1\, \mathring{A}= 10^{-10} m$. The size of the hydrogen atom is about $0.5\, \mathring{A}$ The total atomic volume in $m ^{3}$ of a mole of hydrogen atoms would be

• A. $3.15 \times 10^{-7} m ^{3}$
• B. $3.0 \times 10^{-8} m ^{3}$
• C. $3.85 \times 10^{-7} m ^{3}$
• D. $2.85 \times 10^{-7} m ^{3}$

Answer 1

Answer: (A)

Radius of hydrogen atom $(r)=0.5\, \mathring{A}=0.5 \times 10^{-10} m$
Volume of each hydrogen atom $(V)=\frac{4}{3} \pi r^{3}$
$=\frac{4}{3} \times 3.14 \times\left(0.5 \times 10^{-10}\right)^{3}$
$=5.234 \times 10^{-31}\, m ^{3}$
Number of atoms in one mole of hydrogen
$=$ Avogadro number $(N)$
$=6.023 \times 10^{23}$
$\therefore $ Atomic volume of 1 mole of hydrogen atoms $(V')$
$=$ Volume of a hydrogen atom $\times$ Number of atoms
$V' =V \times N$
$=5.236 \times 10^{-31} \times 6.023 \times 10^{23} m ^{3}$
$=3.152 \times 10^{-7} m ^{3}$