\documentclass[a4paper]{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage{multicol}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tcolorbox}
\usepackage{fancyhdr}
\usepackage{tabularx}
\usepackage{mhchem}

\pagestyle{fancy}
\fancyhead[LO,LE]{Organic Analysis}
\fancyhead[CO,CE]{Andrew Lorimer}

\setlength\parindent{0pt}

\begin{document}

  \title{Organic Analysis}
  \author{Andrew Lorimer}
  \date{}
  \maketitle

  \section{Mass Spectrometry}

    \textbf{Separation of particles by mass}

    Identifies molecules by searching for:
    \begin{enumerate}
      \item The molecular ion \ce{M+}
      \item Fragments of the molecule (as ions)
    \end{enumerate}

    Complicated by noise from different isoptopes of elements (related to relative abundance of isotopes). Every molecule has a \textit{unique} mass spectrum which can be used to identify a substance.

    \subsection*{Process}

    \begin{enumerate}
      \item Sample species are bombarded with electrons
      \item Positive ions are formed by detaching electrons
      \item Ions are accelerated by an electric field
      \item Accelerated ions are deflected by a magnetic field in a circular radius
    \end{enumerate}

    \[ \text{deflection radius} \propto \dfrac{m}{z} \]

    \begin{align*}
      \therefore \qquad \uparrow \text{mass} & \implies \downarrow \text{deflection} \implies \uparrow \text{radius} \\
      \uparrow \text{charge} & \implies \uparrow \text{deflection} \implies \downarrow \text{radius}
    \end{align*}

    \subsection*{Reading a mass spectrum}

    \(x\) axis: mass-charge ratio \(\frac{m}{z}\) of fragments \\
    \(y\) axis: relative abundance of fragments (molecular MS) or isotopes (isotopic MS) with that \(\frac{m}{z}\)
    
    \begin{itemize}
      \item Most ions have a single +ve charge, \therefore \(\frac{m}{z} = m\)
      \item Ions with double or triple +ve charges can show up in lower abundance as \(\frac{m}{2}\) or \(\frac{m}{3}\)
      \item \textbf{Base peak}: most abundant ion, assigned 100
      \item \textbf{Molecular ion}: molecule as singly charged ion \ce{M+}
      \item \textbf{Molecular fragments}: can show functional groups and other characteristic combinations of elements
    \end{itemize}

    \subsubsection*{Combined techniques}

  \section{IR Spectroscopy}

  \section{Magnetic resonance imaging}


\end{document}
