# Introduction to Spectroscopy¶

## Definition¶

Spectroscopy - The study of matter and it’s interaction with light, sound or particles (radiation)

- Can be through absorption, emission or scattering

## What is light?¶

- Light is EM radiation, consisting of an electric field and a perpendicular magnetic field
- Light travels at varying speed through a medium, being energy/wavelength dependent

## What is matter?¶

- A substance that has inertia and occupies physical space
- Made up of particles with different mass, charge and size

## Postulates of quantum mechanics¶

- Particles can only exist in discreet states, determined by their amount of energy
- Interactions of particles cause energy to be emitted or absorbed

\[
\Delta E=E_{excited}−E_{ground}
\]

- The frequency \(\nu\) and wavelength \(\lambda\) of the radiation is related to its energy

\[
\Delta E=h\nu=\frac{hc}{\lambda}
\]

## Energy states¶

- Energy states arise from molecular/atomic orbitals.
- The ground state is the lowest energy configuration of the compound
- As energy is increased, the electrons can jump into a higher orbital with a discreet amount of energy, in what’s called the excited state.
- Rotational/vibrational states arise from energy in the bonds of the atom itself

## Waves¶

Consist of four properties:

- \(\nu\) frequency
- \(\lambda\) wavelength
- \(A\) Amplitude
- \(T\) Period

Expressed by the formula:

\[
y=A\sin\bigg(\frac{2\pi x}{\lambda} + 2\pi \nu t\bigg)
\]

## Energy equation¶

Where:

- \(c=3\times10^8 m\cdot s^{−1}\)
- \(h=4.135\times 10^{−15} \text{ or } 6.626×\times10^{−34} J\)

\[
\Delta E=h\nu=\frac{hc}{\lambda}
\]

## Wavelength¶

\[
\lambda=\frac{c}{n\nu}\approxeq\frac{c}{\nu}
\]

## Wavenumber¶

\[
\bar{\nu}=\frac{1}{\lambda}
\]