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Q.
The diameter of oxygen atom is $3 \,\mathring{A}$. The fraction of molecular volume to the actual volume occupied by oxygen at STP is
AMUAMU 2009
Solution:
The volume of an oxygen molecule has been taken as $2$ times that of one oxygen atom In $22.4\, L$ ie $22.4 \times 10^{-3} m ^{3}$ their are
$N_{A}=6.23 \times 10^{23}$ molecules
Total volume of oxygen molecules
$=2 \times \frac{4}{3} \pi r^{3} \times N_{A}$
$22.4 \times 10^{-3} m^{3}$ is occupied by $N_{A}$ molecules.
$\therefore $ Fraction of volume occupied
$=\frac{2 \times \frac{4}{3} \pi\left(1.5 \times 10^{-10}\right)^{3} \times 6.2 \times 10^{23}}{\left(22.4 \times 10^{-3}\right)}$
$=8 \times 10^{-4}$