Atomic nucleus

(Atomic nucleus of helium.)

The atomic nucleus refers to the region located in the center of an atom made up of protons and neutrons (nucleons). The size of the nucleus (of the order of a femtometer, ie 10^-15 meters) is approximately 100,000 times smaller than that of the atom (10^-10 meters) and concentrates almost all of its mass. The nuclear forces acting between nucleons are about a million times greater than the forces between atoms or molecules. An unstable nucleus is said to be radioactive, it is subject to transmutation, either spontaneous or caused by the arrival of additional particles or electromagnetic radiation.

Physical characteristics

The atom has a lacunar structure, that is to say that between the electrons and the nucleus there is only vacuum, quantum vacuum therefore not really empty since of non-zero energy.

Composition and structure

The nucleus of an atom is made up of particles called nucleons (positively charged protons, and electrically neutral neutrons) strongly bonded together (except for ¹H hydrogen, whose nucleus is simply made up of a single proton) . Its cohesion is ensured by the strong interaction, the main force in the nucleus, which holds the nucleons together and prevents them from moving away from each other.

To model this attraction between nucleons, we can define a nuclear binding energy that can be calculated from the Bethe-Weizsäcker formula.

Two nuclear models can be used to study the properties of the atomic nucleus:

• the layered model;
• the model of the liquid drop.

Isotopes

Isotopes are atoms with the same number of protons (same atomic number Z) but a different number of neutrons.

A chemical element is characterized by the number of protons that make up its nucleus, precisely called the atomic number and noted Z. An atom having as many electrons as protons, which explains its electrical neutrality, Z is also the number of electrons of such an element.

For the same element, we find in nature different nuclides with different numbers of neutrons. These nuclei are called isotopes of the element with this atomic number. The mass number A of an atom is the total number of nucleons (protons and neutrons) that make up a nucleus. The number of neutrons N is equal to A – Z.

A nuclide X is therefore a nucleus characterized by its mass number A and its atomic number Z; it is denoted ^A_ZX (read X A, the atomic number being implicit).

For example, hydrogen ¹₁H, deuterium D or ²₁H, and tritium T or ³₁H are three isotopes of hydrogen.

In practice, the atomic number Z is generally omitted because it is redundant with the chemical symbol, to keep only the notation ^AX. Thus, if we take the example cited above, ordinary hydrogen, deuterium, and tritium are most often noted: ¹H, ²H, and ³H.

Different isotopes of the same element have similar chemical properties, because they depend mainly on its number of electrons. However, their distinct atomic mass allows them to be separated using a centrifuge or mass spectrometer.

Isotopes are also differentiated by their stability and their half-life (or radioactive half-life): isotopes with a deficit or surplus in neutrons are often more unstable, and therefore radioactive. For example, carbon 12 (the most common) and carbon 13 are perfectly stable, while carbon isotopes “heavier” than ¹³C are radioactive (like carbon 14, with a half-life of 5730 years) or “lighter” than ¹²C (like carbon 11, with a half-life of 20 minutes). Note that there are also elements for which all isotopes are unstable, such as technetium or promethium.

Isomers

Nuclear isomers are atoms with identical numbers of protons and neutrons (and which therefore belong to the same isotope) but which exhibit different energy states. This is usually the result of a different organization of the nucleons within the nucleus. The state with the lowest energy is called the “ground state”, and any state with the highest energy is called the “excited state”.

When the distinction is necessary, isomers other than the ground state are identified by the letter “m” added after the mass number and possibly followed by a number if there are several excited states for the isotope in question. Thus, aluminum 26 has two isomers denoted ²⁶Al for the ground state and ^26mAl for the excited state. Another example, tantalum 179 has no less than seven isomers.

In general, excited states are very unstable, and rapidly undergo an isomeric transition which brings them to the ground state (or a less energetic excited state) and during which the excess energy is evacuated as a photon. There are exceptions, however, and some excited states of some isotopes may have a longer half-life than the corresponding ground state (such as tantalum 180m or americium 242m).

Atomic mass

The isotopic atomic mass of an element is the mass corresponding to N_A nuclides of this same isotope, N_A being the Avogadro number (approximately 6.022 04 × 10²³).

Definition: the mass of N_A atoms of carbon 12 is exactly 12 g.

The atomic mass of a chemical element is the weighted average of the atomic masses of its natural isotopes; some chemical elements have very long-lived radioactive isotopes, and therefore their natural isotopic composition, as well as their atomic mass, changes over long periods of time, such as geological eras. This is particularly the case for uranium.

Stability

Binding energy

Some nuclei are stable, that is to say that their binding energy is sufficient, then making their lifespan unlimited. Others are unstable and tend to spontaneously transform into a more stable nucleus by emitting radiation. This instability is due to the large number of nucleons which decreases the unit energy of each bond in the nucleus, making it less coherent. The (spontaneous) transformation by radioactivity always results in an increase in the average binding energy of the nucleons concerned.

There are 3 types of radioactivity, depending on the type of particle emitted:

• α radioactivity if it emits one or more nucleons (proton, neutron or α particle)
• β radioactivity if it emits an electron or a positron with a neutrino.
• These two types of radioactivity are most often accompanied by gamma radiation (emission of photons).

Example:

• uraniums 235 and 238 have higher half-lives than their respective “families” before leading to stable isotopes of lead.
• nitrogen 16 (16 nucleons, 7 protons, 9 neutrons) transforms into oxygen 16 (16 nucleons, 8 protons, 8 neutrons) a few seconds after its creation by beta radioactivity: the weak interaction transforms one of the neutrons in the nucleus into a proton and an electron, thus changing the atomic number of the atom.

Number of nucleons

The stability of an atomic nucleus depends on the nature and the number of nucleons which compose it.

Stable nuclei (152) have been found to have a higher frequency if they are composed of an even number of protons (Z) and neutrons (N). This number increases to 55 for Z even and N odd and to 52 for Z odd and N even. There are only a few stable nuclei with odd number of protons and number of neutrons.

There are also magic numbers (number of protons and / or number of neutrons) for which the natural abundance of stable isotopes is greater: 2, 8, 20, 28, 50, 82, 126. This is the case for example of the helium nucleus, doubly magic, corresponding to the alpha particle emitted by certain nuclei.

Half-life

The half-life of an isotope is the period after which, statistically, half of the atoms in an initial sample will have decayed. Nuclei can have very different half-lives, in fact spanning the entire time range.

A nucleus is considered to be an element (as opposed to a resonance) when its lifespan is long enough for an electronic procession to have time to form (i.e. ~ 10^-15 s)

Stable core

In fact, so-called stable nuclei are only stable insofar as their lifespan approaches that of the proton, the only (meta?)stable baryon. The proton would have, according to the theory, a half-life of approximately 10³³ years, but the experiments carried out to measure this decay of the proton, true cornerstone of the matter, did not verify this prediction: the proton would be more stable than planned.

Size and shape

The radius of a nucleon is of the order of 10⁻¹⁵ m, or 1 fm (femtometer), the term radius being understood here in the sense of having a significant probability of detecting the nucleon in the volume of space considered. As a first approximation, it is generally considered that the radius r of a nucleus of mass number A is (liquid drop model) r = r₀³√A, with r₀ = 1.4 fm. Note when A is small, especially less than 16, r₀ can be equal to 1.2 fm.

This is less than 0.01% of the total radius of the atom. The density of the nucleus is therefore considerably greater than that of the atom itself. It is roughly constant for all nuclei in their ground state (not excited): about 200 million tonnes per cm3 (2 × 10¹⁴ g · cm^-3), density of nuclear fluid.

The actual size and shape of a specific nucleus is highly dependent on the number of nucleons that make it up, as well as their energy state. The most stable nuclei generally have a spherical shape at rest and can take, for example, the shape of an ellipsoid if they are excited. Quite strange shapes can be observed depending on the states of excitement, pear, saucer, even peanut.

In the case of halo nuclei, a few nucleons can have clearly distended wave functions, thus surrounding with a halo the more compact nucleus formed by the other nucleons. Lithium 11 seems, for example, to be composed of a lithium 9 nucleus (the most stable isotope) surrounded by a halo of two neutrons; its size is then close to that of lead 208, which has 20 times more nucleons.

The heaviest stable nucleus consists of 82 protons and 126 neutrons: it is lead 208. The heavier elements are all unstable. Up to the uranium included, they are all naturally present on Terra, elements with atomic number greater than uranium or present in trace amounts can be synthesized in the laboratory. The heaviest element known to date has 118 protons: it is the oganesson.