Particles

Structure of a atom

Symbol Name Charge Mass
p Proton $+1$ ($1.60*10^{-19}$) $1$ ($1.67*10^{-27}$)
n Neutron $0$ $1$ ($1.67*10^{-27}$)
e Electron $-1$ ($-1.60*10^{-19}$) $\frac{1}{1865}$ ($9.11*10^{-31}$)
Nucleon Number - $A$
Relative atomic mass
Protons and neutrons
Proton Number - $Z$
Atomic number
Protons only
Isotopes
Different atoms of the same element with the same proton number but different nucleon numbers
Specific charge
$\frac{charge}{mass}$
Electrons have a higher specific charge than protons, so deflect more in magnetic fields

An important equation

\begin{align}E=hf\end{align} Where $E$ is energy, $h$ is planck’s constant, & $f$ is frequency ($Hz$) \begin{align}E\propto\ f\end{align} planck’s constant is, one guessed it, constant; measured in JouleSeconds \begin{align}6.63*10^{-34} Js\end{align}

\begin{align}\frac{c}{f}=\ \lambda\end{align} \begin{align}\frac{speed \, of\,light}{frequency}=wavelength\end{align} Therefore \begin{align}E=\frac{hc}{\lambda}\end{align} \begin{align}E=mc^2\end{align}

\begin{align}mc^2=\frac{hc}{\lambda}\end{align} \begin{align}mc=\frac{h}{\lambda}\end{align} \begin{align}\lambda=\frac{h}{x}\end{align}

If an electron needs to move from A to B: \begin{align}V=W/Q\end{align} Where voltage is equal to the work done per unit charge \begin{align}W=QV\end{align} \begin{align}1eV=1.6*10^{-19}\end{align}

Particle interactions

Four properties conserved in particle interactions

  • Charge is always conserved
  • Baryon number is always conserved
  • Strangeness is conserved in any interaction other than weak
  • Lepton number is always conserved but must be conserved separately (specific to each lepton)

To check if a neutrino or anti-neutrino is required, check the lepton numbers.

$N$ $\rightarrow$ $P$ $+$ $e^-$ $+$ $\bar{ve}$
$udd$ $\rightarrow$ $uud$ $+$ $e^-$ $+$ $\bar{ve}$
$d$ $\rightarrow$ $u$ $+$ $e^-$ $+$ $\bar{ve}$

Feynman diagrams

Beta negative decay

1

Electron - proton collision

2

Electron Capture

4