
An isotope is an atom with the same number of protons but a different number of neutrons in its nucleus.Isotopes are 'twin brothers' of chemical elements. They have the same number of protons but different numbers of neutrons, so they behave almost identically in chemistry but may have different masses. For example, all carbon atoms have 6 protons, but carbon-12 and carbon-14 are isotopes with 6 and 8 neutrons, respectively.
After the discovery of radioactivity by Becquerel in 1896, Ernest Rutherford and Frederick Soddy showed in 1902 that radioactive decay is accompanied by the transmutation of elements. In 1913, Soddy introduced the term 'isotope' for chemically indistinguishable radioelements with different masses. That same year, J.J. Thomson discovered neon isotopes of masses 20 and 22. The discovery of the neutron by James Chadwick in 1932 explained the existence of isotopes. Today, the study of isotopes underlies a multitude of methods: from radiocarbon dating to nuclear medicine.
The difference in neutron number leads to a difference in nuclear binding energy, which determines stability. According to the liquid drop model and the Weizsäcker formula, the binding energy depends on Z and A. Radioactive isotopes decay according to the radioactive decay law N(t)=N₀e^{-λt}. Mass spectroscopy allows separating isotopes by mass-to-charge ratio. Quantum effects such as tunneling explain α-decay. The Pauli principle governs the filling of nuclear shells, and neutron resonances play a role in neutron capture.
Carbon-14 helps archaeologists determine the age of ancient finds. It is radioactive and gradually decays, so by measuring how much remains, one can find out when the organism died.
| t | variable | elapsed time — time second |
| λ | variable | decay constant — decay constant per second |
| N_0 | variable | initial number of radioactive nuclei — number of nuclei |
| N | variable | current number of radioactive nuclei — number of nuclei |
| ln | operator | natural logarithm of the ratio — natural logarithm |







