# Are all atomic collisions elastic? If this is the case, why?

In kinetic theory of gases it is considered all atomic collisions to be elastic. But if collisions are non-elastic the molecules must lose energy.

• No, some energy can go to the electrons around one atom, like in a He:Ne laser – Ofek Gillon May 21 '17 at 3:34
• A deuterium-proton collision at sufficiently high energies is quite inelastic, producing a helium nucleus. – Robin Ekman May 21 '17 at 15:27

Are all atomic collisions elastic? If this is the case, why?

No, this is one of the key approximations for an Ideal Gas.

I will quote you the very first line on that page word for word; it says "An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interaction is perfectly elastic collision."

Why do we need to make this approximation you might well ask?

The answer is basically so that we can apply the Equation of State to real gases which enables us to calculate their thermodynamic quantities such as the Temperature, Pressure of the gas or its Internal Energy (but for an ideal gas the internal energy is purely kinetic energy for reasons I will explain below).

I won't go into the details too much but depending how far you want to take this you can approximate real gases even better by Van der Waals equation.

As mentioned in the comment real gas molecules (when we don't approximate the gas as 'ideal') lose or gain kinetic energy (a non elastic collision) when they collide.

Not part of your question but real gas molecules also have potential energy due to intermolecular forces between the molecules (which are assumed to be zero for an ideal gas).

The kinetic energy of a moving atom $K~=~\frac{1}{2}mv^2$ has to be comparable to the atomic levels for the collision to be inelastic. The Rydberg levels of a hydrogen atom are $E_n~=~-13.6eV/n^2$, for $n$ the atomic level. For a transition from the $N~=~2$ level to the $n~=~1$ level the energy released is $\Delta E~=~E_2~-~E_1$ $=~10.2eV$ This energy is $16.3\times 10^{-19}j$. The temperature by the equipartition theorem $E~=~\frac{3}{2}kT$ is then $7.9\times 10^4K$ That is fairly hot. To excite a hydrogen atom requires a fairly high temperature.

The assumption of the elastic collision then means the kinetic energy of the atoms are small enough so the inner electronic structure of the atom is not perturbed.