How hot can one heat a single atom?

Question

Imagine a single hydrogen atom in an infinite vacuum being hit by thermal radiation from all directions. Then we crank up the heater, increase the radiation, and continue to do so without limit.
Q1. Does the atom move in a consistent direction? Does it actually move faster at all?
Q2. Does the atom have a limit to the non-kinetic thermal energy it can store?

Then imagine we capture the single atom in a canister, and measure the pressure of that canister.
Q3. Is the portion of the atoms energy measurable as pressure, also unbounded?

And last, does the answer change if the system is a hydrogen molecule instead of a hydrogen atom?

Answer 1

Heat is a thermodynamic concept, applicable to systems with large number of particles (taking Avogadro number $N_A\propto 10^{23}$ as a typical number of particle sin the system). In fact, mathematically statistical physics is valid in thermodynamic limit, $N\rightarrow \infty$.

So, there is no point to talk about heating a single atom.

We can supply energy to atom, raising electrons to higher and higher energy levels, until we reach ionisation. Then the electron and the nucleus separate, and the hydrogen atom ceases to exist. (Although for other atoms, and even for heavy hydrogen, we could still talk about their ions or nuclei.)

Answer 2

I'll start with question #1:

For the radiation to have any effect on the hydrogen atom, it must have a frequency (and therefore a well-defined energy content) that the atom is capable of responding to. For monatomic hydrogen this will be the binding energy of the electron in its orbital, and if irradiated with photons of that energy, the electron will get knocked out of its orbit and then the hydrogen atom isn't an atom any more- it becomes a positive ion consisting of a single proton.

Answer 3

I have to begin by being pedantic. Thermodynamics (the subfield of physics where temperatures, entropy, and pressures are explained) does not make statements about the state of a single atom. Like quantum mechanics, thermodynamics makes statements about the probability of a variety of outcomes. The distinction doesn't matter for systems with a lot of degrees of freedom (a box containing a gas with $10^{23}$ atoms), but the distinction may be important here.

In an answer in this question: "Partition function of a hydrogen gas," user genneth explains that there is a subtlety when we try to apply thermodynamics to a single hydrogen atom. It turns out that in infinite free space, the hydrogen atom is always ionized at at any finite nonzero temperature, because there are infinitely many states with energy very close to 0, but only one groundstate. So even if each ionized state is much less probable than the groundstate, there are so many of them that the total probability of being ionized is 1. In order to get sensible answers, you must put the hydrogen atom in a finite sized box.

So now with all that aside, we can make statements about the distribution of states we expect to find hydrogen atoms in which are each stored in some finite sized box with walls of a temperature T. If T is comparable to the groundstate energy of Hydrogen: $13\,\mathrm{eV}/k_B=150000\,\mathrm{K}$, the hydrogen atom has a very high probability of being ionized - the electron will leave the proton. Because of the issue mentioned in paragraph 2, the temperature at which a significant portion of the atoms will be ionized is likely to be much lower. Typically plasmas of hydrogen are created closer to $3000\,\mathrm{K}$.

Close to that limit, there will also be a significant fraction of hydrogen atoms found in excited states - although for hydrogen the energy difference between the groundstate and the first excited state is not so different from the energy needed to ionize the atom.

At temperatures far below that limit, yes the hydrogen atoms will be found in the electronic groundstate, but they will be found in motion. Actually, the thermodynamic analysis of an ideal gas assumes that the atoms in the gas don't interact. So we can actually look at the thermodynamic solution for an ideal gas to make statements about the average kinetic energy of the hydrogen atoms stored by themselves in boxes. For example, the most probable speed of hydrogen atoms will be $\sqrt{2k_BT/m}$. The average speed will be $\sqrt{8k_BT/\pi m}$. The root-mean-squared speed will be $\sqrt{3k_BT/m}$.

Similarly, if the temperature is well above the ionization temperature, you simply have two free particles, still behaving more or less like an ideal gas. But now there are two free particles instead of one free hydrogen atom. So the pressure would be $(2/V)k_BT$. Is it measurable? I mean not with realistic means of measuring pressure, but it is pressure. Also, with only one box, of course your "pressure" would consist of individual collisions of your particles against the wall you are measuring the force against. So there would be significant "shot noise," and you would have to average over some time to measure the average force.

Something more exotic happens when the temperature becomes comparable to the mass of the electron: $m_ec^2/k_B=6\times 10^{9}\,\mathrm{K}$. When the electron or proton collides with the walls (which I assume are magical and can contain relativistic particles), they can create new electron/positron pairs. So now there will be a distribution of numbers of particles.