# Atomic Nucleus

Protons are found in the nucleus of an atom and each proton has an amount of charge equal to the fundamental unit of charge (e = 1.6 × 10−19 C).1 We denote this fundamental unit of charge as “+1 e” or simply “+1” for the proton. Protons have a mass of approximately one atomic mass unit (amu). The atomic number (Z) of an element is equal to the number of protons found in an atom of that element. As such, it acts as a unique identifier for each element because elements are defined by the number of protons they contain. For example, all atoms of oxygen contain eight protons while all atoms of gadolinium contain 64 protons. While all atoms of a given element have the same atomic number, they do not necessarily have the same mass.

Neutrons are neutral as they have no charge. A neutron’s mass is only slightly larger than that of the proton, and together, the protons and the neutrons of the nucleus make up almost the entire mass of an atom.

Every atom has a characteristic mass number (A), which is the sum of the protons and neutrons in the atom’s nucleus. A given element can have a variable number of neutrons; thus, while atoms of the same element always have the same atomic number, they do not necessarily have the same mass number. Atoms that share an atomic number but have different mass numbers are known as isotopes of the element. For example, carbon (Z = 6) has three naturally occurring isotopes: 612C, with six protons and six neutrons; 613C, with six protons and seven neutrons; and 614C, with six protons and eight neutrons. The convention ZAX is used to show both the atomic number (Z) and the mass number (A) of atom X.

Electrons move through the space surrounding the nucleus and are associated with varying levels of energy. Each electron has a charge equal in magnitude to that of a proton, but with the opposite (negative) sign, denoted by “−1 e” or simply “–e.” The mass of an electron is approximately 1/2000 that of a proton. Because subatomic particles’ masses are so small, the electrostatic force of attraction between the unlike charges of the proton and electron is far greater than the gravitational force of attraction based on their respective masses. Electrons move around the nucleus at varying distances, which correspond to varying levels of electrical potential energy. The electrons closer to the nucleus are at lower energy levels, while those that are further out (in higher shells) have higher energy. The electrons that are farthest from the nucleus have the strongest interactions with the surrounding environment and the weakest interactions with the nucleus. These electrons are called valence electrons and they are much more likely to become involved in bonds with other atoms because they experience the least electrostatic pull from their own nucleus. Generally speaking, the valence electrons determine the reactivity of an atom. The sharing of these valence electrons in covalent bonds allows elements to fill their highest energy level to increase stability. In the neutral state, there are equal numbers of protons and electrons; losing electrons results in the atom gaining a positive charge, while gaining electrons results in the atom gaining a negative charge.

Two forces are at work in the nucleus are the nuclear force and the electromagnetic force. The nuclear force binds the nucleons together, and therefore contributes to the binding energy.1 The electromagnetic force is due to electrostatic repulsion between the positively charged protons in the nucleus. The nucleus stays together because the nuclear force is much stronger than the electromagnetic repulsion.

Mnucleons = Matom + binding energy/c2

Mnucleons > Matom because some of the Mnucleons is converted to binding energy that holds the nucleons together

Mnucleons = mass of all the nucleons that make up the atom in their free, unbound state

Matom = mass of the atom

Mnucleons – Matom = mass deficit (also called mass defect, ΔM)

Binding energy = ΔM c2

Energy liberated = binding energy

The conservation of mass and energy states that the total mass and energy before a reaction is always the same as the total mass and energy after the reaction. If the total mass before the reaction is different from the total mass after the reaction, then the difference in mass is made up for by energy. The difference in mass before and after a reaction is called the mass deficit or mass defect. The energy that makes up for the mass deficit is calculated by:

E = mc2

Energy is liberated when mass is lost during a reaction and energy is absorbed when mass is gained during a reaction. Binding energy most commonly refers to nuclear binding energy (the energy that binds the nucleons together).1 Binding energy per nucleon is strongest for Iron (Fe 56). Binding energy per nucleon is the weakest for Deuterium (the 2-nucleon isotope of hydrogen).

Certain isotopes are unstable and their nuclei break apart, undergoing nuclear decay. Sometimes the product of that nuclear decay is unstable itself and undergoes nuclear decay, too. Naturally occurring radioactive isotopes decay in three primary ways: Alpha particle emission, beta particle emission and gamma radiation emission.2 Alpha decay is the ejection of a helium nucleus at relatively low speed from a radioactive element. It is the weakest form of radiation and can be stopped by a sheet of paper.

Beta decay (negative) is the ejection of a high speed electron from a radioactive element. It has more energy than an alpha particle but it can be stopped by aluminium foil.

Gamma decay is the release of high energy electromagnetic wave from a radioactive element. It is the strongest form of radiation and it can be reduced by a thick layer of lead or concrete.

Conservation of mass dictates that total atomic weight before the decay equal the total atomic weight after and conservation of charge dictates that the total atomic number before the decay equal the total atomic number after. The half-life of a radioactive element is the time it takes for the amount of something to half due to decay.2 After 1 half-life, the amount of the original element decreases by half. After 2 half-lives, the amount of the original element decreases by a factor of 4 and after 3 half-lives, the amount of the original element decreases by a factor of 8. When a compound or element is stable, it doesn’t decay. Decay only occurs if the compound or element is unstable. The more unstable it is, the shorter the half-life.

Semi-log plots are graphs that are used to convert exponential curves into straight lines.2 An exponential curve that curves up becomes a straight line with a positive slope while if it curves down, it becomes a straight line with a negative slope. For exponential decay, a semi-log plot graphs the log of amount vs. time. For exponential decay, a semi-log plot is a straight line with a negative slope. The semi-log plot intercepts the x axis where the original y value is 1

One tool used to identify specific atomic structures is mass spectroscopy, which is based on the concept that differences in mass cause differences in the degree of bending that occurs in a beam of ions passing through a magnetic field.

A mass spectroscope separates isotopes of the same element based on differences in their mass.2 The intensity on the photographic plate indicates the amount of each particular isotope. Other collectors may be used in place of the photographic plate to collect and interpret these data.

References

1) Cook, N. D. (2010). Models of the Atomic Nucleus. Unification Through a Lattice of

Nucleons, 13 – 20.