Q. The diameter of oxygen atom is $3\mathring{\mathrm{A}}$. The fraction of molecular volume to the actual volume occupied by oxygen at STP is

A) $6 \times 10^{- 28}$
B) $8 \times 10^{- 4}$
C) $4 \times 10^{- 10}$
D) $4 \times 10^{- 4}$
Explanation

(b) Neglecting bond length, the volume of an oxygen molecule has been taken as 2 times that of one oxygen atom.
In $22.4\ litres\ i.e.,\ 22.4 \times 10^{- 3}m^{3},$ there 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
$= \frac{2 \times \frac{4}{3} \times \pi \times \left( 1.5 \times 10^{- 10} \right)^{3} \times 6.2 \times 10^{23}}{(22.4 \times 10^{- 3})} = 8 \times 10^{- 4}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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