OCR A-Level Physics/Fields, Particles and Frontiers of Physics/Particle Physics

The Nuclear Atom

Diagram of Rutherford's scattering experiment, also known as the Geiger-Marsden experiment

In 1908, Ernest Rutherford had identified alpha radiation emitted by radioactive materials consisted of fast-moving, positively charged particles. In Rutherford's scattering experiment, a beam of alpha particles were sent through gold foil to observe how they deflected. A fluorescent screen detector emitted flashes of visible light when hit by alpha particles. The results showed that the vast majority of the alpha particles travelled straight through the gold foil without being deflected. A small number were deflected through angles less than 90 degrees. One in every eight thousand alpha particles was deflected at an angle greater than 90 degrees, meaning it would effectively 'bounce back' in the direction which it came.

Deductions

The Ernest Rutherford experiment led to the following conclusions;

• The majority of the mass of the atom is within the nucleus
• The nucleus has a positive charge
• The nuclear diameter is considerably smaller than the diameter of the atom, therefore the atom is mainly empty space

The diameter of the nucleus is around ${\displaystyle 10^{-14}}$ mm and the diameter of the atom is around ${\displaystyle 10^{-10}}$ mm.

Model of the Atom

Niels Bohr proposed that electrons can only occupy certain energy levels, or shells. Later, Rutherford proposed the name proton for the positively charged particle in the nucleus of an atom. In 1932, James Chadwick discovered the neutron.

Particle Charge / ${\displaystyle e}$  Mass / u
Proton 1 1
Neutron 0 1
Electron -1 1/1840

Atomic Notation

The atomic number is the number of protons within the nucleus, this is often denoted by ${\displaystyle Z}$

The nucleon number, ${\displaystyle A}$ , is the number of protons and neutrons found in the nucleus of an atom.

Isotopes are the same element that contains different number of neutrons.

An atom can be represented by ${\displaystyle {}_{Z}^{A}\!X}$ , where ${\displaystyle X}$  is the element symbol, we can say that the number of protons = ${\displaystyle Z}$ , the number of electrons = ${\displaystyle Z}$ , and the number of neutrons = ${\displaystyle A-Z}$

Strong Nuclear Force

Force between nucleons

The attractive force is responsible for keeping the nucleus together cannot be the gravitational force of attraction because the force is too small and around ${\displaystyle 10^{36}}$  times smaller than the size of the electrostatic force of repulsion. Since the electrical force between two protons is a force of repulsion and the force of gravity is far too small to keep them together, we know there must be a different lind of force acting between protons, called the strong nuclear force.

Properties of strong nuclear force

The strong nuclear force decreases rapidly with distance, and doesn't extend beyond adjacent prints and neutrons within the nucleus. The force must act between nucleons, and is independent of charge. Some of the properties are as follows:

• The force is repulsive and attractive
• It provides a repulsive force between nucleons up to a separation distance of ${\displaystyle 0.5*10^{-15}}$ m
• It's an attractive force between ${\displaystyle 3*10^{-15}}$ m and ${\displaystyle 0.5*10^{-15}}$
• Beyond ${\displaystyle 3*10^{-15}}$ m the strong nuclear force approaches 0

Equilibrium Separation

For two neutrons to be in equilibrium, the resultant force must equal zero. Neutrons have no charge, no electrical charge, and negligible gravitational charge, we focus on the strain nuclear charge for answers.

When th strong nuclear force equals zero, they have separation ${\displaystyle d}$ . If ${\displaystyle d}$  increased then a large force of attraction would pull them back. If ${\displaystyle d}$  decreased then a large force of repulsion would push them back into equilibrium

Nuclear Density

As we know the atom diameter is around 10 000 times greater than the diameter of the nucleus. Following that the density of the atom as a whole should be considerably smaller than the density of the nucleus's the vast majority of the mass is contained within the nucleus.

The relationship between the radius of the nucleus and the nucleon number isn't linear. Experiments have shown that the relationship between the nuclear radius, ${\displaystyle R}$ , and the nucleon number ${\displaystyle A}$ , is given by ${\displaystyle R=r_{0}A^{1 \over \ 3}}$ , where ${\displaystyle r_{0}}$  is a constant. So the radius is directly proportional to the cube root of the mass number. ${\displaystyle r_{0}}$  is has the value of ${\displaystyle 1.4*10^{-15}}$

Nuclear density

Density is defined as mass per unit volume and nuclear density is stated as ${\displaystyle \rho ={m_{n} \over \ V}}$ , where ${\displaystyle m_{n}}$  is the mass of the nucleon. This leads to: ${\displaystyle \rho ={m_{n}A \over \ (4\pi \ {r_{0}}^{3})A/3}}$

Simplifying this gives the equation for the mean density of the nucleus given by ${\displaystyle \rho ={m_{n} \over \ (4\pi \ {r_{0}}^{3})}}$ . All the values in the equation are constants at nucleon level and independent of the mass number. This means that all atomic nuclei have the same density.

Fundamental Particles

Classification of particles

Subatomic particles are divided into two main groups - Hadrons and Leptons

Hadrons are composed of quarks. Quarks are fundamental particles, meaning they can't be broken down into smaller particles. Protons and neutrons are hadrons and are both composed of three quarks. All hadrons experience a strong nuclear force.

Leptons are fundamental particles, for example an electron is a lepton. Each lepton has it's own neutrino. All leptons experience a weak nuclear force but do not experience the strong nuclear force.

Antiparticles

Every particle has its own 'opposite particle' called an antiparticle. An electrons antiparticle is the positron. All antiparticles have the same mass as the particle, but the opposite charge.

When particles interact with their antiparticles they annihilate each other, with their combined mass is converted into energy.

Quark Properties

Beside having mass, and charge, quarks also have other properties such as strangeness, charm, baryon and lepton numbers, and spin. Each one has a number that measures this.

The three quarks that were initially proposed were the up, down and strange quarks. We can see from the table their properties:

Quarks Antiquarks
types up down strange anti-up anti-down anti-strange
symbol ${\displaystyle u}$  ${\displaystyle d}$  ${\displaystyle s}$  ${\displaystyle {\bar {u}}}$  ${\displaystyle {\bar {d}}}$  ${\displaystyle {\bar {s}}}$
charge ${\displaystyle Q}$  ${\displaystyle +{2 \over \ 3}e}$  ${\displaystyle -{1 \over \ 3}e}$  ${\displaystyle -{1 \over \ 3}e}$  ${\displaystyle -{2 \over \ 3}e}$  ${\displaystyle +{1 \over \ 3}e}$  ${\displaystyle +{1 \over \ 3}e}$
strangeness ${\displaystyle S}$  0 0 -1 0 0 +1
baryon number ${\displaystyle B}$  ${\displaystyle 1 \over \ 3}$  ${\displaystyle 1 \over \ 3}$  ${\displaystyle 1 \over \ 3}$  ${\displaystyle -{1 \over \ 3}}$  ${\displaystyle -{1 \over \ 3}}$  ${\displaystyle -{1 \over \ 3}}$

Using this model of quarks and antiquarks we can see how certain particles and antiparticles are constructed

• A proton, uud, has charge (${\displaystyle {2 \over \ 3}+{2 \over \ 3}-{1 \over \ 3})e=+e}$ , baryon number 1, strangeness 0
• A neutron, udd, has charge (${\displaystyle {2 \over \ 3}-{1 \over \ 3}-{1 \over \ 3})e=0}$ , baryon number 1, strangeness 0

Decay of particles

The quark nature of nucleons can be used to explain beta-plus and beta-minus radioactive decay. Many unstable hadrons decays due to weak interaction by transformation of their component quarks.