Matter and Radiation

Inside the Atom

All atoms contain:

More information about these particles are below:

Isotopes

Atoms with the same number of protons but different number of neutrons.

The nucleon number is the number of nucleons in a nucleus while the atomic number is the number of protons. These units are used for organising the elements on the periodic table.

Specific Charge

The specific charge of a charged particle is defined as its charge divided by its mass. For example:

Worked Example

A nucleus of Helium has a charge of $+1.60 \times 10^{-19}\,C $ and a mass of $1.67 \times 10^{-27}\,kg $.

$$ \eqalign{
\text{Specific charge} &= \frac {charge}{mass} \\
&= \frac {1.60 \times 10^{-19}}{1.67 \times 10^{-27}} \\
&= 9.58 \times 10^{7}\,Ckg^{-1}}$$

Stable and Unstable Nuclei

A stable isotope has nucleons that do not disintegrate, as there is the strong nuclear force. This overcomes the electrostatic repulsion between the nucleus and the protons. For the strong nuclear force:

strong_force

Radioactive Decay

Naturally occurring isotopes release three types of radiation:

$$ ^{A}_{Z}X \rightarrow\,^{A-4}_{Z-2}Y +\,^{4}_{2}\alpha $$

$$ ^{A}_{Z}X \rightarrow\,^{~~~~A}_{Z+1}Y +\,^{~~0}_{-1}\beta + \overline{\nu} $$

Photons

Visible light is a small part of the electromagnetic spectrum, which is made up of many types of waves of different wavelengths.

Type Wavelength Type Wavelength
Radio > 0.1m Ultraviolet 400nm- 1nm
Microwave 0.1m - 1mm X-rays < 1nm
Infrared 1mm - 700nm Gamma rays < 1nm
Visible 700nm- 400nm

To calculate the frequency or wavelength of a wave, the following equation can be used, where $\lambda$ is the wavelength, $f$ is the frequency and $c$ is the speed of light ($3 \times 10^{8}\,ms^{-1}$):

$$ \lambda = \frac {c}{f} $$
When electromagnetic waves are emitted from beta decay, they are emitted as small bursts of energy known as photons. The energy of a photon can be calculated by:

$$ \text{photon energy E} = hf $$

where $E$ is the energy, $f$ is the frequency and $h$ is a constant referred to as the Planck constant ($6.63 \times 10^{-34}\,J$).

Antiparticles

Antimatter

All particles have a corresponding antiparticle. These are particles that share the exact the same properties as the matter particle except for the charge and the spin. For example an antiproton is a negatively charged particle with the same mass as the proton.

Particle Charge Antiparticle Charge
proton ($p$) +1 antiproton ($\overline{p}$) -1
neutron ($n$) 0 antineutron ($\overline{n}$) 0
electron ($e$) -1 positron ($e^{+}$) +1
electron-neutrino ($\nu_{e}$) 0 electron-antineutrino ($\overline\nu_{e}$) 0

Pair production and Annihilation

When energy is converted into mass, equal amounts of matter and antimatter are produced. This is process is called pair production. If one gamma ray photon passes close by a nucleus, a particle and corresponding antiparticle can be produced.

pair_production

The opposite process is where a particle and its corresponding antiparticle collide, converting the mass back into energy.

annihilation

Classification of Particles

Particles can be divided into certain groups deepening on their properties.

Hadrons

Hadrons are particles that experience the strong nuclear force and are composed of smaller particles called quarks. Hadrons are subdivided into two groups:

hadrons

Leptons

Leptons are fundamental particles that don't feel the strong nuclear force. Examples of leptons include the stable electron ($e^{-}$) and unstable muon ($\mu^{-}$) and tau ($\tau^{-}$) which both decay into electrons.

Neutrinos are also leptons, with a different neutrino for electrons ($\nu_{e}$), muons ($\nu_{\mu}$) and tau leptons ($\nu_{\tau}$). Neutrinos have negligible mass, no charge and only interact through the weak interaction.

Quarks

Quarks are fundamental particles which when arranged together, form hadrons. Three types of quarks, up ($u$), down ($d$) and strange ($s$) have different properties that give the hadrons certain properties. Strange quarks have a property called strangeness.

Name Symbol Charge Baryon Number Strangenss
up $u$ $+\frac{2}{3}$ $+\frac{1}{3}$ 0
down $d$ $-\frac{1}{3}$ $+\frac{1}{3}$ 0
strange $s$ $-\frac{1}{3}$ $+\frac{1}{3}$ -1
Name Symbol Charge Baryon Number Strangenss
anti-up $\overline{u}$ $-\frac{2}{3}$ $-\frac{1}{3}$ 0
anti-down $\overline{d}$ $+\frac{1}{3}$ $-\frac{1}{3}$ 0
anti-strange $\overline{s}$ $+\frac{1}{3}$ $-\frac{1}{3}$ +1

Quark Composition of Baryons

Baryons are composed of three quarks.

Antiprotons are $\overline{u}\overline{u}\overline{d}$ and antineutrons are $\overline{u}\overline{d}\overline{d}$.

Quark Composition of Mesons

Mesons are made up of a quark and an antiquark. As $K$ mesons have strangeness, they include a $s$ meson.

mesons

Conservation Laws

When interactions occur, certain laws must be obeyed:

Exchange Particles

For an interaction to occur, an exchange particle called a gauge boson must be exchanged between particles. There are four fundamental forces, each with its own gauge boson.

Interaction Gauge Boson Particles Affected
strong gluon hadrons
electromagnetic photon charged particles
weak $W^{+}$, $W^{-}$, $Z^{0}$ all
gravity graviton all

The larger the mass of the gauge boson, the shorter the range of the force. The $W$ boson involved in the weak interaction has a mass 100 times that of a photon meaning it only has a very small range. A photon on the other hand has a zero mass, therefore has an infinite range.

Feynman Diagrams

Feynman diagrams can be used to show interactions. On these diagrams:

Some interactions are shown below:

Beta Decay

b_decay

In beta decay, an up quark changes into a down quark which changes a proton into a neutron, or a down quark changes into a up quark, turning a neutron into a proton. An antineutrino is formed in $\beta^{-}$ decay and a neutrino in $\beta^{+}$ decay in order to conserve the lepton number.

$$ n \rightarrow p + e^{-} + \overline{\nu}_{e} \\
p \rightarrow n + e^{+} + \nu_{e} $$

Electron Capture

electron_capture

In electron capture, an inner shell electron interacts with a proton from the nucleus.

$$ p + e^{-} \rightarrow n + \nu_{e} $$

Neutrino-Baryon Interaction

neutriono_baryon

In the interaction between neutrinos and baryons, the baryon changes and an electron or positron is released.

$$ n + \nu_{e} \rightarrow p + e^{-} \\
p + \overline{\nu}_{e} \rightarrow n + e^{+} $$

© Andrew Deniszczyc, 2018