# 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¶

$\bar{\nu}=\frac{1}{\lambda}$