Different types of radioactive decay are characterized by their changes in mass number as well as atomic number, according to the radioactive displacement law of Fajans and Soddy. 
For example, uranium-238 usually decays by alpha decay, where the nucleus loses two neutrons and two protons in the form of an alpha particle.  Thus the atomic number and the number of neutrons each decrease by 2 (Z: 92 → 90, N: 146 → 144), so that the mass number decreases by 4 (A = 238 → 234); the result is an atom of thorium-234 and an alpha particle ():
On the other hand, carbon-14 decays by beta decay, whereby one neutron is transmuted into a proton with the emission of an electron and an antineutrino.  Thus the atomic number increases by 1 (Z: 6 → 7) and the mass number remains the same (A = 14), while the number of neutrons decreases by 1 (N: 8 → 7).  The resulting atom is nitrogen-14, with seven protons and seven neutrons:
Beta decay is possible because different isobars have mass differences on the order of a few electron masses. If possible, a nuclide will undergo beta decay to an adjacent isobar with lower mass. In the absence of other decay modes, a cascade of beta decays terminates at the isobar with the lowest atomic mass.
Another type of radioactive decay without change in mass number is emission of a gamma ray from a nuclear isomer or metastable excited state of an atomic nucleus. Since all the protons and neutrons remain in the nucleus unchanged in this process, the mass number is also unchanged.