# The Nucleus

Nuclear chemistry is the study of changes in the nuclei of atoms. A nucleus consists of two types of nucleons—protons and neutrons—that are held together by the strong nuclear force.

Many fields of chemistry look at the interactions between atoms. In chemical reactions, bonds between atoms break, and new bonds form. Chemical reactions do not involve changes in the atomic nucleus. Nuclear chemistry is the field of chemistry that studies changes in atomic nuclei. The nucleus can gain or lose particles, or particles in the nucleus can change into other particles. Because elements are defined by the number of protons in the nucleus, which is the atomic number, any change in atomic number changes the element.

The nucleus of an atom is made up of positively charged protons and neutral neutrons. The protons and neutrons have comparable masses. Both protons and neutrons have a much greater mass than electrons. A nucleon is a proton or a neutron in an atomic nucleus.

### Masses of Subatomic Particles

Particle Symbol Mass (amu, atomic mass unit)
Proton \begin{aligned}{}_1^1\rm {p}\end{aligned} 1.007276
Neutron \begin{aligned}{}_0^1\rm {n}\end{aligned} 1.008665
Electron ${}_{-1}^{\;\;\,0}{\rm{e}}$ 0.000549

Subatomic particles are represented with symbols and have specific masses.

Two fundamental forces of the universe play major roles in the nucleus. The strong nuclear force is the short-range force that acts between protons and neutrons, keeping the nucleus together. Its range is so short that it acts only between nucleons that are close together. The second fundamental force that acts on nucleons is the electromagnetic force, a repulsion between positively charged protons. This repulsion is weak compared to the strong nuclear force. However, the electromagnetic force can act at much greater distances. Each proton in the nucleus repels all other protons, not just the neighboring ones.

In nuclear chemistry, the number of neutrons in a nucleus is important. A nuclide is an atomic nucleus with a specific number of protons and neutrons. Nuclides are represented in the form of ${}_Z^A\rm {X}$ where A is the atomic mass, Z is the proton number (atomic number), and X is the element symbol. This representation allows for calculation of the number of neutrons, N, through the formula $N+Z=A$. For example, nitrogen-14 is represented by ${}_{\,\,7}^{14}\rm {N}$ and nitrogen-15 is represented by ${}_{\,\,7}^{15}\rm {N}$. The term isotope is often used interchangeably with the term nuclide. Isotopes are nuclei with the same number of protons but different numbers of neutrons.

Neutrons are stable in a nucleus. Outside of a nucleus, they are not stable and eventually decay into a proton, releasing an electron. The decay of a neutron into a proton and an electron can be written as an equation.
${}_0^1\rm{n}\rightarrow{}_1^1\rm{p}+{}_{-1}^{\;\;\,0}{\rm{e}}$

### Mass Defect

Nucleons in a nucleus have lower energy than nucleons outside of a nucleus, resulting in a mass defect. Einstein's mass-energy equivalence relates mass and energy.

The difference between the total mass of the individual nucleons that make up a nucleus and the actual mass of the nucleus is called mass defect. Mass defect occurs because nucleons in a nucleus are more stable and have lower potential energy than nucleons outside of a nucleus. Consider a helium atom with two protons and two neutrons. Each proton has a mass of 1.007276 amu, so the total proton mass is 2.014552 amu. Each neutron has a mass of 1.008665 amu, so the total neutron mass is 2.017330. Altogether the mass of the helium atom is 4.031882 amu. This is different from the experimentally determined mass of the helium nucleus, which is 4.00151 amu. The mass difference is $4.031882-4.00151=0.03037\;{\rm{amu}}$. This difference in mass is not unique to helium. The total mass of the individual nucleons that make any nucleus is greater than the mass of the nucleus itself. The energy that binds nucleons manifests as a difference in mass. Energy and mass are directly proportional; when energy decreases, so does mass. It requires energy to break a nucleus apart. The energy required to break a nucleus into its component nucleons is the nuclear binding energy.

Mass and energy are related to each other. The equation that relates energy and mass, known as the mass-energy equivalence equation, was formulated by the German physicist Albert Einstein. It defines the relationship between energy E in joules (J), mass m in kilograms (kg), and the speed of light c in meters per second (m/s).
$E=mc^2$
The nuclear binding energy and mass-energy equivalence can be used to calculate the nuclear binding energy. The sum of mass and energy is always conserved. For example, the nuclear binding energy for helium can be calculated using the mass difference.
\begin{aligned}E&=mc^2\\&=(0.03037\;{\rm{amu}})\left(\frac{1\;\rm {g}}{6.022\times10^{23}\;{\rm{amu}}}\right)\left(\frac{1\;{\rm{kg}}}{{1}\rm{,}000\;\rm {g}}\right)\left(2.9979\times10^8\,\frac{\rm{m}}{\rm{s}}\right)^2\\&=4.534\times10^{-12}\,\frac{{\rm{kg}}\cdot\rm{m}^2}{{\rm{s^2}}}\\&=4.534\times10^{-12}\;\rm{ J}\end{aligned}
Mass was determined to 0.03038 amu by solving for the mass difference. Mass is converted to kg using dimensional analysis. The speed of light c is $2.9979\times{10}^8\;{\rm{m/s}}$, which is a constant. Using these values, energy in joules can be determined.

### Stability of Nuclei

Nuclei are most stable when their neutron-to-proton ratio is close to one. When the neutron number versus proton number is graphed for all known isotopes, a zone of stable isotopes is at the center.

Two opposing forces act within an atomic nucleus. The strong nuclear force is a attractive, short-range force that acts between all nucleons—the charged protons as well as the neutral neutrons. The electromagnetic force is a repulsive force that acts between positively charged protons. Adding protons to a small nucleus increases both the attractive strong nuclear force and the repulsive electromagnetic force. Adding neutrons to a small nucleus increases only the attractive strong nuclear force.

The short range of the strong nuclear force means nucleons can form a limited number of strong nuclear attractions. As the nucleon count increases, the strong nuclear force increases linearly. Electromagnetic force is not limited by range. Every proton added will repulse every other proton. As proton count increases, electromagnetic force increases exponentially. Because of this difference, nuclei above 270 nucleons are very unstable. The largest nuclei that has been observed has 294 nucleons.

The ratio N:Z (where N is the neutron number and Z is the number of protons or atomic number) is significant with respect to nuclear stability. A graph of neutron number versus proton number for all known isotopes shows certain patterns:

• For small atoms, with a proton number up to 20, the N:Z ratio of the most stable isotope is about 1:1. As the nucleus gets larger, the number of neutrons in the most stable isotope increases faster than the number of protons. The most stable isotope of gold, for example is ${}_{\;79}^{197}{\rm{Au}}$, giving a N:Z ratio of 1.49.
• The zone of stability, or band of stability, is the region that represents stable, nonradioactive isotopes on a graph of the neutron number versus the proton number for all known isotopes.
• Nuclei above the zone of stability are rich in neutrons and are unstable.
• Nuclei below the zone of stability are rich in protons and are unstable.

#### Zone of Stability

A more detailed analysis of stable nuclei yields more patterns. For example, if a nucleus has an even number of protons and an even number of neutrons, it is more likely to be stable. Nuclei with odd numbers of protons and odd numbers of neutrons are unlikely to be stable. Nuclei with an even number of protons but an odd number of neutrons, or vice versa, fall in between. A magic number is a specific number of protons or neutrons that makes a nucleus more likely to be stable. The magic numbers are proton numbers of 2, 8, 20, 28, 50, or 82 or neutron numbers of 2, 8, 20, 28, 50, 82, or 126.

These patterns can be partially explained by the shell model of the nucleus, a model that defines the locations of protons and neutrons in shells that are partially analogous to electron shells. According to the shell model, pairs of neutrons or pairs of protons represent a more stable arrangement, similarly to what is seen with pairs of electrons.

### Nuclear Decay

Unstable nuclei break down into smaller nuclei over time by radioactivity.

The process by which unstable nuclei break down into other, smaller nuclei over time, releasing particles and/or energy, is radioactivity, or radioactive decay. An isotope with an unstable nucleus that experiences radioactive decay is called a radioisotope. There are different types of radioactive decay, depending on the properties of the nuclei undergoing it.

Radioactive decay often involves antiparticles. An antiparticle is a particle with the same mass as an elementary particle, but with the opposite charge. The antiparticle of an electron (${}_{-1}^{\;\;\,0}{\rm{e}}$) is a positron (${{}_{+1}^{\;\;\,0}{\rm{e}}}$), which has the same mass as an electron and a positive charge equal in magnitude to the negative charge of an electron. The antiparticle of a proton is an antiproton. An antiproton has the same mass as a proton and has an equivalent-magnitude, but negative, charge. Matter consisting of antiparticles such as antiprotons, antineutrons, and positrons is called antimatter. Antimatter, and antiparticles, annihilate when they interact with matter and elementary particles. The energy released in such an annihilation can be calculated by mass-energy equivalence, $E=mc^2$.

Nuclei above the zone of stability have an overabundance of neutrons relative to the number of protons. In such a nucleus, one of the neutrons is likely to decay into a proton. A high-energy electron is released when a neutron decays into a proton in the nucleus, called the beta particle (${{}_{-1}^{\;\;\,0}\beta}$). This type of radioactivity is called beta decay. Carbon-14 decays into nitrogen through beta decay.
${}_{\;\;6}^{14}\rm{C}\rightarrow{}_{\;\;7}^{14}\rm{N}+{}_{-1}^{\;\;\,0}\beta$
Note that this decay increases the proton number, or atomic number, of the nucleus, thus changing its identity from carbon to nitrogen. Beta decay reduces the neutron number and increases the proton number, making a nucleus approach the band of stability. In other words, emission of a beta particle makes an unstable nucleus become more stable. Nuclei below the band of stability have an overabundance of protons, and too few neutrons. In such a nucleus, a proton is likely to change into a neutron. In this case, an antiparticle, a positron (${}_{+1}^{\;\;\,0}{\rm{e}}$) is emitted. For example, neon-19 decays into fluorine by emitting a positron.
${}_{10}^{19}{\rm{Ne}}\rightarrow{}_{\;9}^{19}\rm{F}+{}_{+1}^{\;\,\,0}\rm{e}$
Positron emission reduces the neutron number and increases the proton number, making a nucleus approach the zone of stability. Electron capture is another process that converts a proton in the nucleus to a neutron. In this nuclear change, the nucleus captures an electron (${}_{-1}^{\;\;\,0}{\rm{e}}$). For example, potassium-40 nuclei can capture an electron to become argon.
${}_{19}^{40}\rm {K}+{}_{-1}^{\;\,\,0}\text{e}\rightarrow{}_{18}^{40}\rm{Ar}$
Electron capture is the reverse process of beta decay. In electron capture, as in positron emission, the proton number increases and a nucleus approaches the zone of stability. A large nucleus may undergo alpha decay to lose nucleons. During alpha decay, an alpha particle is lost from the nucleus. An alpha particle ($\alpha$) is a particle identical to a helium ion (He2+) that is emitted during the decay of radioactive elements. It is made up of two protons and two neutrons. An alpha particle is represented in a nuclear equation by the symbol ${}_2^4{\rm{He}}$. Alpha particles do not contain any electrons. Uranium-238, for example, decays into thorium-234 through alpha decay.
${}_{\;\,92}^{238}\rm {U}\rightarrow{}_{\,\;90}^{234}\rm{Th}+{}_2^4{\rm{He}}$
An alpha particle decreases both the proton and the neutron numbers. A nucleus that is above the zone of stability typically undergoes alpha decay to approach the zone of stability.

A gamma ray, or gamma radiation, is high-energy electromagnetic radiation. Gamma rays are energy emitted by the nucleus as it becomes more stable through radioactivity. Gamma rays are symbolized by the lowercase Greek letter gamma: $\gamma$ or ${}_0^0\rm\gamma$. Gamma rays do not change the proton or neutron numbers and are commonly not written in nuclear reactions.