Transmutation describes a process by which the nucleus of a radioactive atom undergoes decay into an atom with a different number of protons, until such time as a stable nucleus is produced.

An alpha particle (i.e., a helium nucleus) is released during alpha decay of a radioactive substance. An element with a lower mass is formed. Mass is not conserved. Atomic mass number (or nucleon number, or baryon number) is conserved.

Beta decay (beta negative decay) occurs when a beta (negative) particle is released from the nucleus (i.e., electron). Mass is also not conserved in beta decay. Nucleon number is conserved. In beta decay, the beta particle released originated in the nucleus of the atom, not in the electron orbital. A neutron is lost, and in its place a proton and an electron are formed.

Gamma decay is the release of excess stored energy from the nucleus. No transmutation occurs. However, gamma decay often accompanies alpha and beta negative decay in a decay series. (The series of steps in the transmutations occuring until a stable nucleus results, is called a decay series.) Gamma decay occurs when an excited nucleus (excited by photon or particle bombardment, or it may be a decay product in an excited state) returns to the ground state. An excited nucleus is heavier than the ground state, by a mass equal to the mass/energy equivalent of the energy of the emitted gamma ray.

Each radioactive nuclide emits radioactivity at its characteristic rate, different from that of other nuclides. The rate of radioactive decay is related to the energy change that accompanies the transformation, but it is not a direct relationship. The rate of radioactive emissions of a radioactive nuclide is directly proportional to the amount of radioactive material present. The rate of decay of a radioactive nuclide is measured by its half-life. Half-life is the time required for one half of the atoms in any starting sample of a radioisotope to decay. If the half-life of a radioactive nuclide is known, its decay constant can be calculated by:

l = 0.693 / T_1/2        N_t = N₀e^(-lt)

where N₀ is the starting number of nuclei, N_t is the number of nuclei remaining after time t, l is the decay constant, and e = 2.718. The units for the decay constant would be s^-1 (or sometimes expressed in disintegrations per second) if the half-life is expressed in seconds. This relationship expresses radioactive decay based on statistics and probability, from an examination of the behaviour of a large number of individual situations. Note that it does not give any indication when a particular nucleus will undergo decay, but only the amount of time needed for a certain proportion of the nuclei in the sample to decay.