How many bits of information can be stored in an atom? How many bits of information can be stored in an atom? The atom in question being as big as you like, but must be stable with regard to nuclear decay
 A: Let us restrict ourselves to storing distinguishable information in an atom, rather than using it as part of an extended information storage system (putting it $x$ meters away from another atom can store $\log_2(x/\epsilon)$ bits given a measurement precision of $\epsilon$ meters).
There are several natural properties one can use. One is which isotope it is: there are 254 known stable isotopes, so by selecting which one we can store 7.9887 bits. Another one is electron state: in a hydrogen atom you can put the electron at any principal quantum number $n=1,2,3,\ldots$ which seems it could store any amount of information... but in practice the lifetimes are very short (a few nanoseconds to a few milliseconds) with a few exceptions (one is 10 million years), so the number of stable bits is very limited. Similarly nuclear and electron spin can in principle store a few bits, but usually they are not very stable.
The in-principle limits given by our current understanding of physics is due to the Bekenstein bound (and related entropy bounds). They state that in a finite region of spacetime with a finite amount of energy the number of distinguishable states are finite; see the informal derivation in this post by Scott Aaronson for an idea of why this is plausible. This gives us $$I<\frac{2\pi c}{\hbar }RM$$ for a radius $R$ system of mass $M$ (assuming the self-gravity is weak). For a hydrogen atom I get around 1.58 Mb.
Note that this is an upper bound: it does not tell us that there is any method of actually storing this much information. But we have reasons to think that were you to somehow cram 2 megabytes into a hydrogen atom it would collapse to a tiny black hole or something else would disperse the information.
A: I came here thinking information as something what could build the atom. Reading here I noticed the terms come from different disciplines, so I googled for Information Theory and Physics and got this:
https://en.wikipedia.org/wiki/Physical_information
Found what is a bit related do the physics entropy:

The base of the logarithm used in this definition is arbitrary, since it affects the result by only a multiplicative constant, which determines the unit of information that is implied. If the log is taken base 2, the unit of information is the binary digit or bit (so named by John Tukey); if we use a natural logarithm instead, we might call the resulting unit the "nat." In magnitude, a nat is apparently identical to Boltzmann's constant k or the ideal gas constant R, although these particular quantities are usually reserved to measure physical information that happens to be entropy, and that are expressed in physical units such as joules per kelvin, or kilocalories per mole-kelvin.

So I conclude an atom, representing something to physical world, is related to a bit if the math of your physical system model brings a log of base 2.
Your question then depends of the system what you're observing.
A: I'm thinking that a ferromagnetic atom in a cold cubic crystal could maintain any of six different orientations. The problem would be setting and detection on that scale.
A: According to Planck one proton can contain a thousand - trillion - trillion - trillion - trillion - trillion bits of information. This is the area (not volume) that a black hole expands when you add one bit of information. Information is not lost but information can not escape a black hole. When you erase your hard drive the information still exists as energy. (Leonard Susskind) https://www.youtube.com/watch?v=2DIl3Hfh9tY
