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JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Self Evaluation Test - Kinetic Theory

  • question_answer
    A nitrogen molecule has some rms speed at \[0{}^\circ C\]on the surface of the earth. With this speed, it goes straight up. If there is no collisions with other molecules, the molecule will rise up to a height of               

    A) 82 km

    B) 12.4 km

    C) 10.6 km

    D) 152 km

    Correct Answer: B

    Solution :

    [b] \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times 8.31\times 273}{28\times {{10}^{-3}}}}=493m/s\] Thus \[\frac{1}{2}mv_{rms}^{2}=\frac{mgh}{1+\frac{h}{R}}.\] After substituting the values and simplifying, we get h= 12.4 km


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