Question

The mean free path of nitrogen molecules at a pressure of 1.0 atm and temperature 0⁰C is $0.8 \times 10^{- 7}m$. If the number of density of molecules is $2.7 \times 10^{25}perm^{3}$, then the molecular diameter is

• A. $3.2nm$
• B. $3.2Å$
• C. $3.2\mu m$
• D. $2.3mm$

Answer 1

Answer: (B)

$3.2Å$

Answer 2

Mean free path $\lambda =$ 0.8 × 10^–7 m number of molecules per unit volume $n = 2.7 \times 10^{25}$ per m³

Substituting these value in $\lambda = \frac{1}{\sqrt{2}\pi nd^{2}}$ we get $d = \sqrt{1.04 \times 10^{- 19}} = 3.2 \times 10^{- 10}m$ $= 3.2Å$