Stanton D. answered • 05/03/24
Tutor to Pique Your Sciences Interest
Hi Ivy,
You may use the Maxwell-Boltzmann distribution to visualize this.That gives numbers (or probabilities, equivalently) for particles (as y-axis) as a function of speed (x-axis). Look it up; literature will indicate the mean speed (not velocity!) relationship. However, the "approximate range of velocities" is a mushy question (and not just for the distinction between velocity and speed!). You must set arbitrary cut-offs (such as, >95%-more-than-speed, and >95%-less-than-speed) so as to bracket 90% of atoms by count. Note that these limits require integrating the Maxwell-Boltzmann function, either exactly (if you know calculus) or numerically (such as with an Excel spreadsheet!), in order to find the areas-under-the-curve at the extremes.
However, don't lose any atoms as you count -- once they argon, they argon!
So the M.-B. is what obtains when a known amount of energy is distributed by exchange in elastic collisions among a group of (gaseous molecules). The energy MUST be retained as total kinetic energy! If you want a crude analogy, it's like a classroom of students who all WANT to do well in school, and they're competing (passively!) for their grade, which will be averaged to a "C" or hotter.
Take note of the exact name : there is also the Boltzmann distribution, that's an exponential reflecting probabilities of occupancy of states (y-axis) with a continuum of energy as the x-axis. Not the same! The B. distribution is what obtains when a source of energy MAY be accessed by an individual entity, such as a molecule. Or, the entity MAY dump the energy back to the source. By the crude analogy started above, this is like a classrrom of students who don't WANT to learn anything in school, so they would all stay as "F" grades unless forced somewhat randomly to temporarily learn some bits.
If you discern from this that I've taught in both these classroom analogies, you discern astutely.
-- Cheers, --Mr. d.
