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?
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.