Nuclear transmutation is the conversion of one chemical element or isotope into another, either by nuclear reactions (which requires an external trigger) or by radioactive decay (which are random and spontaneous).
While chemical reactions involve the rearrangement of atoms (to form new compounds), nuclear reactions involve the rearrangement of nucleons (to form new nuclei). While chemical reactions are represented symbolically by chemical equations, nuclear reactions are represented by nuclear equations.
For example, when an alpha-particle (very energetic He-4 nucleus) is smashed against a nitrogen nucleus (N-14), the reactant nucleons undergo a rearrangement to become an oxygen (O-17) and a hydrogen (He-1, or proton) nucleus[1]. This nuclear reaction is represented by the nuclear reaction equation below.
Note that the total mass number of the reactant nuclei (4+14) is the same as the total mass number of the product nuclei (17+1). This is because the total number of nucleons must remain the same in any nuclear reaction.
Similarly, the total atomic number of the reactant nuclei (2+7) is the same as the total atomic number of the product nuclei (8+1). This is because the total electric charge must remain the same in any nuclear reaction.
[1] Historically, this was the nuclear reaction that led to the discovery of the proton.
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