A-level Physics/Nuclear and Particle Physics/The Nucleus

Nucleons

Protons and neutrons in an atomic nucleus. On the periodic table, you can see the number of nucleon written as the mass number.

What force holds the atomic nuclei together?

For many years people had wondered what held an atom in place and how it doesn't just split apart due to repulsive electric forces. At first they thought that it was gravity which held the atom's protons and neutrons in place. This was disproved after they found out gravity was very very weak at nuclear levels. Infact it's a million million million million million million times too small. (10^36)
We now know the interaction responsible for binding quarks, antiquarks, and gluons to make hadrons is called strong force. Residual strong force interactions provide the nuclear binding force. Simply put, strong force is the force that holds atomic nuclei together against the Coulomb (electrostatic repulsion) force of repulsion between protons. The strong force acts on any pair of hadrons.

The radii of atomic nuclei

The following gives the formula to work out the radii of atomic nuclei.
$r=r_0{A}^{\frac{1}{3}}$
Where:

• r is the radii
• A is the number of nucleons

Density of nuclear matter

$density=\frac{mass}{volume}$

$\rho =\frac{m}{\frac{4}{3}(\pi r^3)}$ (since $\frac{4}{3}(\pi r^3)$ is the volume of a sphere, radius r)

Calculating electrostatic force

$F=\frac{1}{4\pi {ϵ}_0}\frac{Q_1{Q}_2}{r^2}$
Where:

• F is the force
• ${ϵ}_0$ is the permittivity of free space with the value 0.8541878176 × 10⁻¹² F/m c(farad per metre)

Calculating gravitional force

$F=G\frac{m_1{m}_2}{r^2}$

Where:

• F is the force
• m1 and m2 are product of the two masses;
• and r being the distance between them.
• G is the value of the gravitational constant, which is

$G=6.67\times 10^{-11}\text{N}{\text{m}}^2{\text{kg}}^{-2}$