How does radioactive decay transmute elements?

Radioactive decay can transmute elements because radioactive decay involves changes in the nucleus of an atom. There are severl types of radioactive decay that result in an atomic nucleus changing from one element into another (transmutation). Let's take a quick look at them.

In beta decay, either a proton in an unstable nucleus changes into a neutron (beta plus decay), or a neutron in an unstable nucleus changes into a proton (beta minus decay). In either case, the nucleus has undergone a change (transmutation), and the new nucleus has one less or one more proton than it had before.

In electron capture, an electron orbiting an unstable nucleus is captured from its orbit by the nucleus, and it "combines" with a proton to form a neutron. The nucleus now has one less proton, and has transmuted.

It might be helpful to include spontaneous fission in this list. In spontaneous fission, a heavy nucleus "splits" into a pair of fission fragments, and each fragment is the nucleus of a new atom.

Perhaps we should add neutron capture to the list. In neutron capture, a neutron (or perhaps more) is captured by an atomic nucleus, and the nucleus becomes momentarily unstable. Depending on the nucleus and the "mechanics" of the capture, the unstable nucleus can then undergo another transformation that has been triggered by the capturing event. This nucleus could simple become stable with an increased neutron count (no transmutation), or could undergo beta decay, or could spontaneously fission.

Links can be found below to related questions for more information. The curious investigator would be well rewarded for following them.