# Q 2.16: The unit of length convenient on the atomic scale is known as an angstrom and is denoted by $\AA : 1\ \AA = 10^{-10} m$. The size of a hydrogen atom is about $0.5 \AA$. What is the total atomic volume in $m^3$ of a mole of hydrogen atoms?

Radius of an Hydrogen atom = 0.5 $\AA$= 0.5 x 10-10 m

Volume = $\frac{4}{3} \pi r^3$

$4/3 \times 22/7 \times (0.5 \times 10^{-10})^3$

= $0.524 \times 10^{-30} m^3$

1 hydrogen mole contains $6.023 \times 10^{23}$ hydrogen atoms.

The volume of 1 mole of hydrogen atom = $6.023 \times 10^{23} \times 0.524 \times 10^{-30}$

= $3.16 \times 10^{-7} m^3 \approx 3 \times 10^{-7} m^3$.

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