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JEE Main 201910 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
10 April
Shift
Morning Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2019 · 10 April · Morning Shift · Physics · Kinetic Theory of Gases

A 25 × 10 ^ - 3 m ^ 3 volume cylinder is filled with 1 mol of O _ 2...

A 25×10−3m325 \times {10}^{- 3}{m}^{3} volume cylinder is filled with 11 mol of O2{O}_{2} gas at room temperature (300K)( 300K ) . The molecular diameter of O2{O}_{2} , and its root mean square speed, are found to be 0.3nm0.3nm and 200m/s200m / s , respectively. What is the average collision rate (per second) for an O2{O}_{2} molecule?

Options

  1. A 1011~ {10}^{11}
  2. B 1012~ {10}^{12}
  3. C 1010~ {10}^{10}
  4. D 1013~ {10}^{13}

Correct answer

B.  1012~ {10}^{12}

Step-by-step solution

Average collision rate =nv−d2π= n\overset{-}{v}{d}^{2}\pi
=6.023×102325×10−3×83π×200×(0.3×10−9)2π≈4×10−12= \dfrac{6.023 \times {10}^{23}}{25 \times {10}^{- 3}} \times \sqrt{\dfrac{8}{3\pi}} \times 200 \times {\left(0.3 \times {10}^{- 9}\right)}^{2}\pi \approx 4 \times {10}^{- 12}
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