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In school we are learning about half-life, and I was wondering if it is possible to decay to half an atom?

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    $\begingroup$ No, much like it is impossible to die to half a man. $\endgroup$ – Ivan Neretin Oct 23 '17 at 19:58
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    $\begingroup$ This is a weird question. When the atom decays, there's still an atom left. In fact, there may be 2. $\endgroup$ – Zhe Oct 23 '17 at 20:12
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    $\begingroup$ @IvanNeretin Well, you could get cut in half; not that unsimilar to fission ;) $\endgroup$ – Mithoron Oct 23 '17 at 23:31
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    $\begingroup$ If I cut a piece of string in half, and discard one of the pieces, am I left with half a piece of string? $\endgroup$ – Dawood ibn Kareem Oct 24 '17 at 3:02
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To clear up what are becoming confusing comments.

An atom is a nucleus of protons and neutrons surrounded by electrons.

An atom can decay by fission to make two or more atoms with a smaller number of protons and neutrons in each new atom. The electrons get distributed between them. Now in physics we'd normally describe this as a nuclear decay, rather than thinking about electrons around the nucleus which, to a certain extent, are irrelevant to the underlying process.

Now depending on how you want to think about this you're either increasing the number of atoms by splitting one into two, or you're creating two (or more) smaller sized atoms which you might loosely describe as halves of the original.

Fission products (the results of fission) do not generally contain exactly half the number of protons and neutrons and electrons in the original atom, even when those numbers are even, so we can't say they're generally exact halves.

Fission can also release neutrons - so a nucleus looses e.g. one neutron but still has the same number of protons left. Even when the split is closer to 50-50, the process can still release some neutrons, and in fact that's exactly what is used in nuclear weapons and reactors.

Another typical decay type is by alpha particle emission. An alpha particle is, in fact, a Helium nucleus, so again that's a split to two different nuclei.

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The photodisintegration of $\ce{^{9}_{4}Be}$ might come close to what you are looking for.

When high energy photons excite a beryllium-9 nucleus it may decay into a neutron and two helium-4 nuclei ($\alpha$ particles). Neglecting the neutron, the latter are roughly half of the original nucleus.

$$\ce{^{9}_{4}Be + \gamma -> 2 ^{4}_{2}He} + n$$

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No. When an atom decays, it splits into two smaller atoms, and its protons are divided between those two new atoms. The smallest number of protons you can split off an atom is one, and a single proton by itself is still a hydrogen atom.

Note that you can split a proton into sub-atomic particles, but this would not be called "decay" anymore.

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    $\begingroup$ A proton splitting spontaneously into other particles would be a proton decay. No one has ever observed a proton decay and it's an open question in physics how long the proton half life is or even if it does decay. Anyone seeing a proton decay, report it at once. :-) $\endgroup$ – StephenG Oct 24 '17 at 1:48

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