Electromagnetic Radiation and Wave Properties

The four wave parameters:

• Wavelength $\lambda$ — the distance of one complete wave (crest to crest); measured in metres, nm or angstrom.
• Frequency $\nu$ — the number of waves passing a given point per second; unit hertz ($\text{Hz} = \text{s}^{-1}$).
• Wavenumber $\bar{\nu}$ — the number of waves per unit length, $\bar{\nu} = \dfrac{1}{\lambda}$; unit $\text{m}^{-1}$ or $\text{cm}^{-1}$.
• Amplitude — the maximum displacement (height) of the wave; it sets the brightness/intensity, NOT the energy of a photon.
• The wave travels at velocity $c$, linking these by $c = \nu\lambda$.

The velocity relation for electromagnetic radiation:

• $c = \nu\lambda$, so $\nu = \dfrac{c}{\lambda}$ and $\lambda = \dfrac{c}{\nu}$.
• $c = 3 \times 10^{8}\ \text{m/s}$ is the same for ALL electromagnetic radiation in vacuum.
• At fixed $c$, frequency and wavelength are inversely proportional: $\nu \propto \dfrac{1}{\lambda}$.
• Keep $\lambda$ in metres so that $\nu$ comes out in Hz (convert nm by $\times 10^{-9}$).

Planck's quantum theory:

• Radiant energy is emitted or absorbed only in whole-number multiples of a quantum: $E = nh\nu$ (n = 1, 2, 3, ...).
• The energy of ONE photon is $E = h\nu = \dfrac{hc}{\lambda}$.
• Energy is directly proportional to frequency and inversely proportional to wavelength: high $\nu$ / short $\lambda$ = high energy.
• Planck's constant $h = 6.626 \times 10^{-34}\ \text{J s}$.
• Energy per mole of photons $= E \times N_A$, where $N_A = 6.022 \times 10^{23}$.

The spectrum in order of increasing frequency and energy (decreasing wavelength):

• Radio waves — longest $\lambda$, lowest $\nu$, lowest energy.
• Microwaves — next up.
• Infrared (IR) — felt as heat.
• Visible light — the only band we see; within it the order is VIBGYOR, red lowest energy, violet highest energy.
• Ultraviolet (UV) — higher energy than visible.
• X-rays — high energy, penetrating.
• Gamma rays — shortest $\lambda$, highest $\nu$, highest energy.