The atomic nucleus is the small, dense central region of an atom. It contains protons and, except in ordinary hydrogen, neutrons, collectively called nucleons. Its positive electric charge attracts the surrounding electrons, while interactions between nucleons hold the nucleus together. Although it occupies only a tiny fraction of an atom’s volume, it contains nearly all its mass. Nuclear composition determines an element’s identity and its isotopic form; nuclear structure and transformations are central subjects of nuclear physics. (energy.gov)
Discovery and historical development
In 1909, Hans Geiger and Ernest Marsden observed that some alpha particles passing through thin metal foils scattered through unexpectedly large angles. In 1911, Ernest Rutherford explained these observations by proposing that an atom’s positive charge and most of its mass were concentrated in a very small central region. This interpretation replaced models in which positive charge was spread throughout the atom. (nobelprize.org)
The discovery of the neutron by James Chadwick in 1932 provided the missing constituent needed to explain nuclear masses without assigning excessive positive charge to nuclei. Proton–neutron models subsequently replaced earlier hypotheses involving electrons inside the nucleus. Later developments in quantum mechanics established nuclear structure as a many-particle quantum problem rather than a miniature classical planetary system. (nobelprize.org)
Composition and notation
The number of protons, (Z), is the atomic number and identifies the chemical element. The neutron number is (N), and their sum,
[ A=Z+N, ]
is the mass number. A nuclear species is commonly written ({}^{A}_{Z}X), where (X) is the element’s chemical symbol. Carbon-12, for example, contains six protons and six neutrons. The mass number counts nucleons; it is not an exact measurement of nuclear mass. (ocw.mit.edu)
Nuclei with the same (Z) but different (N) are isotopes. Their atoms have broadly similar electronic chemistry but can differ substantially in nuclear stability. Ordinary hydrogen has a single-proton nucleus, whereas deuterium contains one proton and one neutron. A neutral atom has (Z) electrons, but losing or gaining electrons changes its ionic charge without changing the nucleus’s elemental identity. (ocw.mit.edu)
Size and nuclear forces
Nuclear dimensions are measured in femtometers, with (1\ \mathrm{fm}=10^{-15}\ \mathrm{m}). For many nuclei, an approximate effective radius is
[ R \approx r_0A^{1/3}, ]
where (r_0) is about (1.2\ \mathrm{fm}). This scaling indicates roughly constant interior nucleon density. A nucleus has no rigid boundary: its density falls gradually near the surface, and its shape may be spherical or deformed. (sibor.physics.tamu.edu)
The nuclear force is a residual manifestation of the strong interaction. At a deeper level, nucleons contain quarks interacting through gluons. Between nucleons, the force is predominantly attractive over short nuclear distances but strongly repulsive at very small separations. It competes with electromagnetic repulsion between positively charged protons. Its short range means that each nucleon interacts most strongly with nearby nucleons, helping explain the approximate saturation of nuclear density and binding. (nobelprize.org)
Binding energy and stability
A bound nucleus has less mass than its constituent free protons and neutrons. The difference corresponds to its nuclear binding energy through mass–energy equivalence:
[ B=\left[Zm_p+Nm_n-M_{\mathrm{nucleus}}\right]c^2. ]
Here (B) is the energy required to separate the nucleus completely into free nucleons, and (c) is the speed of light. (hep.phy.cam.ac.uk)
Binding energy per nucleon generally rises rapidly among light nuclei, reaches its highest values in the iron–nickel region, and declines gradually for heavier nuclei. These trends explain why combining suitable light nuclei or splitting suitable heavy nuclei can release energy. Binding energy alone, however, does not determine whether a particular decay occurs: the masses of the possible products and the transition’s quantum properties also matter. (hep.phy.cam.ac.uk)
Light stable nuclei often have similar proton and neutron numbers. Heavier stable nuclei generally require a neutron excess, which supplies additional nuclear attraction without additional proton–proton repulsion. Pairing effects favor many nuclei with even proton and neutron numbers. (ocw.mit.edu)
Quantum structure and nuclear models
Nuclei possess discrete energy levels and definite quantum properties, including angular momentum and parity. The nuclear shell model describes protons and neutrons occupying quantum states in an average nuclear potential. The Pauli exclusion principle restricts how identical nucleons fill these states. Conventional shell closures occur at the “magic numbers” 2, 8, 20, 28, 50, 82, and 126, although shell patterns can change in nuclei far from stability. (sibor.physics.tamu.edu)
The complementary liquid-drop model describes bulk properties through volume, surface, electrical repulsion, neutron–proton imbalance, and pairing contributions. Collective models account for nuclear rotations and vibrations. These approaches describe different aspects of the same quantum system rather than mutually exclusive physical structures. (ocw.mit.edu)
Decay and nuclear reactions
Unstable nuclei undergo radioactive decay. In alpha decay, a nucleus emits two protons and two neutrons as a helium nucleus. Beta decay changes a neutron into a proton or a proton into a neutron through the weak interaction. Gamma emission lowers nuclear excitation energy without changing (Z) or (A). Decay rates are commonly expressed by a half-life. (energy.gov)
Nuclear fission divides a heavy nucleus into smaller fragments, often releasing neutrons. Nuclear fusion combines light nuclei. Together with particle capture and decay, such reactions participate in nucleosynthesis, which formed light nuclei in the early universe and produces further elements in stars and other astrophysical environments. (energy.gov)