The rms velocity of Nitrogen molecule in a cylinder containing Nitrogen gas at 17⁰C is 5×10¹² m/s. If the diameter of the Nitrogen molecule is roughly 2.0 $\overset{0}{A}$ and no. of molecules per unit volume is 2.56×10²⁵ $m^{- 3}$ . Then the time taken for the collision between two Nitrogen molecules

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3×10^–13 s

2×10^–13 s

1×10^–13 s

4.4×10^–20 s

answer is B.

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Detailed Solution

$t = \frac{λ}{V_{r m s}} = \frac{1}{V_{r m s}} \frac{1}{\sqrt{2} π d^{2} n}$

$\Rightarrow t = \frac{1}{5 \times 10^{12}} \times \frac{1}{1.41 \times 3.14 \times {(2 \times 10^{- 10})}^{2} \times 2.56 \times 10^{25}}$

$t = 4.4 \times 10^{- 20} \sec$

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