Why are all metals not attracted to a magnet?

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The complete answer to this question involves a deep understanding of quantum mechanics and electromagnetic theory, and is quite difficult to explain. Fortunately, there is an easier way, albeit not 100% accurate, that will guide you in the right direction.

All un-ionized atoms at rest have a certain number of protons, having +1 charge each, in the nucleus. The net positive charge from all of the protons creates an electric field surrounding the nucleus which attracts negative charges and repels positive charges. The act of attracting and repelling other charges toward and away from the nucleus requires the protons to use energy, so were this attraction and repellent behavior to continue on indefinitely, the protons would have to keep using energy indefinitely. However, were the protons able to reach an electrically neutral state of equilibrium with another particle, they wouldn't have to keep spending all that energy. Well, those particles do exist, they're called electrons, and sure enough, they and the protons do reach an electrically neutral state of equilibrium by bonding with each other in an equal quantity.

The above wall of descriptive text was a set up, since I'm pretty sure you know that electrons are in atoms, but you should pay attention to a subtle, yet very important idea that I used. There were two states described above, one with no electrons and one with an equal amount of electrons and protons, we'll call them state 1 and state 2 respectively. The system ended up choosing state 2 over state 1, but why? The answer is, as it is so often, energy. State 2, as was explained above, required the overall use of less energy than state 1. We call states like state 2 energetically favorable as opposed to state 1 which was energetically unstable, or simply unstable. Now for the part that would have driven Van Gogh crazy enough to slice off his other ear: The system in state 1 knew that state 2 existed before ever even noticing an electron. In fact, state 1 was doing everything it could possibly do to get to the lower energy state regardless of whether or not it was even feasible; it only cared that it was possible. This might not seem like a big deal, but in fact, it's the reason why EVERYTHING happens. All phenomena that is observable in the universe are only observable because of systems trying to get to a lower energy state, regardless of whether or not it will ever find the means.

This is why some metals aren't attracted to magnets. Those particular metals have reached a state of energy so low already, that the magnet doesn't have the strength to pull them out of it. Now, the way they reached this state is a bit complicated and weird, so I'm not going to go too in depth. Basically, there are shells (think of concentric spherical surfaces existing further and further away from the nucleus) of allowed energy states surrounding the nucleus that electrons are able to populate. Mind you, from quantum mechanics, the electrons can only be in these shells, not between them. Each shell has a maximum number of electrons that are allowed to be in them. Additionally, the most energetically favorable state for the atom would be if it had the exact amount of electrons to fill up one of the shells, no more no less. As discussed before, the atom is going to do whatever it can to get to that point, and, once it's there, try its hardest not to leave. That's the reason why some metals don't magnetize, for to do so, would mean leaving there stable state.

Bismuth, gold, lead, mercury, silver and copper are examples of metals with most, if not all, of their shells closed. Not surprisingly then, they are also examples of metals that don't magnetize.

Lastly, it's important to remember that I'm using a model to describe experimental results. There are no actual physical shells inside an atom, it just helps to think of it that way.
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