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

Nucleons

Protons and neutrons are the constituents of atomic nuclei. A proton is a positively charged particle which has the same charge as an electron, but positive. A neutron, on the other hand, is a neutral particle with zero charge. Protons have a mass of 1.6552e-27 kg and a charge of +1.66e-19 Coulombs, while neutrons have a mass of 1.6725e-27 kg. Protons and neutrons collectively are called NUCLEONS. The number of protons in the nucleus give the atomic number, while the sum of the total mass of protons and neutrons gives 99.9% of the mass of the atom, the rest is due to electrons. 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 why it doesn't just split apart due to repulsive electric forces. At first they thought that it was gravity which held the atoms, protons and neutrons in place. This was disproved after they found out gravity was very very weak at nuclear levels. In fact it's a million million million million million million times too small. (10^36)
We now know the interaction responsible for binding quarks, anti-quarks, and gluons to make hadrons is called strong nuclear force (SNF) or The Strong Interaction. 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. It has an extremely short range of only a few femtometers. Even so, at a very short range indeed, the SNF becomes repulsive, otherwise the neutrons and protons would be attracted together to the point where they would become a singularity.

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
• r0 is a constant having value 1.2 fermi to 1.5fermi.

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 nucleus which is considered as sphere of radius r).NUCLEAR DENSITY is constant throughout the nuclear dimensions.

Calculating electrostatic force

$F={\frac {1}{4\pi \epsilon _{0}}}{\frac {Q_{1}Q_{2}}{r^{2}}}$
Where:

• F is the force
• $\epsilon _{0}$ is the permittivity of free space with the value 8.8541878176^e-12 F/m c(farad per metre per coulomb)

above expression is known as a coulomb law of electrostatics.

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

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