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I've been looking for problems to practice on this topic and found a problem asking to use the Maxwell-Boltzmann distribution function to calculate the fraction of Argon gas molecules with a speed of 305 m/s at 500 K. I thought the distribution function could only be used to find the fraction of molecules moving between two given speeds not at a specific speed. Can someone explain how to do this?

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    $\begingroup$ You're right. The question expects you to find the fraction of molecules with speeds between $v$ and $v+dv$ (in terms of $dv$; there will be a factor of $dv$ in the answer). $\endgroup$ Commented Dec 7, 2013 at 3:59
  • $\begingroup$ @NowIGetToLearnWhatAHeadIs Thanks for clearing that up! $\endgroup$
    – Logan
    Commented Dec 7, 2013 at 16:44

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I don't think you can calculate the fraction for molecules with exactly 305 m/s speed. Statistical calculations have an inherent assumption about the 'precision'. Exact 305 m/s speed implies your precision for calculation of speeds has become infinite. You can only determine speeds upto some precision and hence there will be a 'dv' factor in your final answer.

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