Boltzmann Distribution question?

Question

Why do some molecules have very high energy and why is the curve asymptotic to the horizontal axis?

Answer 1

Let's answer the 2nd question first. The Maxwell-Boltzmann distribution is "asymptotic to the horizontal axis" because that's another way of expressing that the number of molecules with nearly infinitely high energies are nearly non-existent. In other words, the probability of finding such molecules drops down to 0 with higher energies.

Why they exist at all in the first place is more interesting to explain, and maybe this analogy would help. Let's say that I have N coins, and I throw all of them, and note the number of heads and tails. You will find that a small difference is more likely than a large difference, but it's not impossible that all N coins have turned up heads, which means a very large difference. It can happen, but it's very rare. Molecules acquire their speeds through random collisions with other molecules, and, as with the coins, it's possible that with successive collisions, a molecule can acquire a very high velocity, but it is rare. For molecules in a 3D gas, the Maxwellian-Boltzman distribution expresses the likelihood of finding molecules of different energies, with a average energy corresponding to the hump of the distribution.