<P> The proton, the electron, and the neutron are classified as fermions . Fermions obey the Pauli exclusion principle which prohibits identical fermions, such as multiple protons, from occupying the same quantum state at the same time . Thus, every proton in the nucleus must occupy a quantum state different from all other protons, and the same applies to all neutrons of the nucleus and to all electrons of the electron cloud . However, a proton and a neutron are allowed to occupy the same quantum state . </P> <P> For atoms with low atomic numbers, a nucleus that has more neutrons than protons tends to drop to a lower energy state through radioactive decay so that the neutron--proton ratio is closer to one . However, as the atomic number increases, a higher proportion of neutrons is required to offset the mutual repulsion of the protons . Thus, there are no stable nuclei with equal proton and neutron numbers above atomic number Z = 20 (calcium) and as Z increases, the neutron--proton ratio of stable isotopes increases . The stable isotope with the highest proton--neutron ratio is lead - 208 (about 1.5). </P> <P> The number of protons and neutrons in the atomic nucleus can be modified, although this can require very high energies because of the strong force . Nuclear fusion occurs when multiple atomic particles join to form a heavier nucleus, such as through the energetic collision of two nuclei . For example, at the core of the Sun protons require energies of 3--10 keV to overcome their mutual repulsion--the coulomb barrier--and fuse together into a single nucleus . Nuclear fission is the opposite process, causing a nucleus to split into two smaller nuclei--usually through radioactive decay . The nucleus can also be modified through bombardment by high energy subatomic particles or photons . If this modifies the number of protons in a nucleus, the atom changes to a different chemical element . </P> <P> If the mass of the nucleus following a fusion reaction is less than the sum of the masses of the separate particles, then the difference between these two values can be emitted as a type of usable energy (such as a gamma ray, or the kinetic energy of a beta particle), as described by Albert Einstein's mass--energy equivalence formula, E = mc, where m is the mass loss and c is the speed of light . This deficit is part of the binding energy of the new nucleus, and it is the non-recoverable loss of the energy that causes the fused particles to remain together in a state that requires this energy to separate . </P>

Who discovered atoms of the same element are identical