Atoms can be split apart in a few different ways. An atom can divide in to two smaller atoms when it is hit with a fast neutron, or sometimes just randomly. This is how nuclear decay and nuclear power work.
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Atoms can also lose electrons and become ions if you ‘excite’ them by giving them energy using another electron or a photon.
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We also use particle colliders (like CERN in Switzerland) to make atoms hit each other at very high speeds and break apart so we can look at their sub-atomic structure.
Splitting an atom is actually not correct.
Atoms are made of a positively charged nucleus that is surrounded by a cloud of negatively charged electrons. What is split is the atomic nucleus, the core of an atom.
The nucleus is made of neutrons and protons. To many of either and the forces that keep the nucleus together become unbalanced.
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