Ncert Exercises & Solutions

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

Radius of hydrogen atom, r = 0.5 Å= 0.5 × $10^{- 10} m$

Volume of hydrogen atom = $\frac{4}{3} {πr}^{3}$

$= \frac{4}{3} \times \frac{22}{7} \times {(0.5 \times 10^{- 10})}^{3}$
$= 0.524 \times 10^{- 30} m^{3}$

According to Avogadro’s hypothesis, one mole of hydrogen contains :
N = 6.023 x 10²³ atoms
So, Atomic volume of 1 mole of hydrogen atoms,
V=N X Volume of hydrogen atom ,
or, V= 6.023 x 10²³ x 0.524 x 10^-30
= 3.156 x 10^-7m³ ≅ 3 x 10^-7 m³

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