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The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $Å: 1 Å=10^{-}$ ${ }^{10} \mathrm{~m}$. The size of a hydrogen atom is about $0.5 Å$. What is the total atomic volume in $\mathrm{m}^3$ of a mole of hydrogen atoms?
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Verified Answer
Given, $r=0.5 Å=0.5 \times 10^{-10} \mathrm{~m}$
Volume of each atom of hydrogen $=\frac{4}{3} \pi \mathrm{r}^3$ $=\frac{4}{3} \times 3.14\left(0.5 \times 10^{-10}\right)^3=5.236 \times 10^{-31} \mathrm{~m}^3$
No. of atoms in 1 mole of $\mathrm{H}_2=6.023 \times 10^{23}$
(Avogadro Number)
$\therefore$ Atomic volume
$$
=5.236 \times 10^{-31} \times 6.023 \times 10^{23}
$$
$$
=3.154 \times 10^{-7} \mathrm{~m}^3 \text {. }
$$
Volume of each atom of hydrogen $=\frac{4}{3} \pi \mathrm{r}^3$ $=\frac{4}{3} \times 3.14\left(0.5 \times 10^{-10}\right)^3=5.236 \times 10^{-31} \mathrm{~m}^3$
No. of atoms in 1 mole of $\mathrm{H}_2=6.023 \times 10^{23}$
(Avogadro Number)
$\therefore$ Atomic volume
$$
=5.236 \times 10^{-31} \times 6.023 \times 10^{23}
$$
$$
=3.154 \times 10^{-7} \mathrm{~m}^3 \text {. }
$$
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