Why Electrons Stay Hot and the Gas Stays Cool

In an elastic collision, a light particle bouncing off a much heavier one keeps almost all of its energy — think of a ping-pong ball hitting a bowling ball. An electron is thousands of times lighter than any gas atom, so each collision transfers only a tiny fraction ΔE/E ≈ 4m/M of its energy to the heavy particle. Switch gases and watch the difference: the atoms change size with their true mass, and the recoil scales as 1/M — light helium gets visibly nudged by each hit, heavier nitrogen barely shifts, and heavy argon stands almost perfectly still while the electron ricochets at full speed.

Mass ratio M / me
Max energy lost per collision
Collisions to thermalize (order)

The fraction is the elastic-collision limit ΔE/E = 4mM/(m+M)², which for m ≪ M reduces to about 4m/M. Because that number is so small, an electron must undergo thousands of elastic collisions before it shares its energy with the gas — and in a short-lived or low-power discharge it simply never gets the chance. Real collisions also include inelastic channels (excitation, ionization) that drain electron energy differently; this model isolates the elastic mass effect that sets the two-temperature character of cold plasma. On-screen ion recoil is exaggerated for visibility; the relative recoil between the three gases is kept true to 1/M.