Electromagnetic (EM) radiation arises from oscillating **electric** and **magnetic** fields. It can be considered either as a stream of quanta (photons, particles) or waves.

### EM radiation as waves

Concerning the wave aspect, it is a sinusoidally varying electric and magnetic field vector with the peaks pointing at right angles to one another and perpendicular to the direction the wave is travelling.

#### Definitions:

Amplitude (A) | peak field strength | |

Wavelength (λ) | distance between successive peaks | Units = m (metres) |

Time (T) | time between successive peaks | Units = seconds |

Frequency (f) | the number of peaks passing a given point in one second | f = 1/T Units = s ^{-1} (per second) or Hz (hertz, 1Hz = 1 cycle per second) |

Velocity (c) | the speed calculated as the distance traveled by a peak in one second | velocity = frequency x wavelength v = f x λ |

### EM radiation as particles

When considering EM radiation as particles, the particles are small packets, or quanta, of energy called **photons** that travel in straight lines. The energy of the photon packet is measured in joules (J) but this is inconveniently small when describing EM radiation so the unit of **electron-volt** is used.

1 ev = 1.6 x 10^{-19} J

#### Intensity

The intensity (i.e. photon energy or field strength) is related to the characteristics of the wave by **Planck’s ****constant**.

E = hf

Key:

E = photon energy

h = Planck’s constant (6.63 x 10-34 m2kg/s)

f = frequency

Rearranging the earlier equation of velocity = fλ and assuming that the velocity is fixed (i.e. 1) gives you:

f = 1 / λ

In other words, the frequency is inversely proportional to the wavelength. Substituting this into the Planck’s constant equation gives you:

E = h / λ

i.e. the photon energy is inversely proportional to the wavelength.

#### Key points

- As the frequency increases, so does the energy of the wave (directly proportional)
- As the wavelength increases the energy of the wave decreases (inversely proportional)

Written by radiologists, for radiologists with plenty of easy-to-follow diagrams to explain complicated concepts. An excellent resource for radiology physics revision.

### Definitions

**Photon fluence = **number of photons per unit area at a given time and given cross-section of beam (e.g. number of photons in area A or B)

**Energy fluence = **total amount of energy of photons at a given time at a given cross-section of the beam per unit area (total energy of photons in area A or B)

**Energy fluence rate (aka beam intensity) = **total energy per unit area passing through a cross section per unit time (watts/mm^{2}) (total energy per second of photons in area A or B).

### Inverse square law

As the beam moves further from the source the area of the beam increases. The area of the beam is equal to the distance squared.

A ∝ d^{2}

Key:

A = area

d = distance

This means the same number of photons are spread over a larger area and the strength of the beam decreases (the intensity is inversely proportional to the area).

intensity ∝ 1 / A

Putting the two equations together gives:

intensity ∝ 1 / d^{2}

This relationship between the distance from the source and the energy of the beam is called the **inverse square law** as the intensity is inversely proportional to the distance from the source squared.

However, this law only strictly applies if:

- Beam comes from point source
- No scatter or absorption of the beam

## Electromagnetic spectrum

(scroll sideways to view whole table)

Extremely low frequency | Radiowaves | Microwaves | Infrared | Visible light | Ultraviolet | X-rays | Gamma rays | |

Source | Power line | AM and FM radios | Microwave oven | Radiant heat | Sun | Arc wielding | X-ray tubes | Radioactive sources |

Wavelength | km | cm-km | mm-m | microns-mm | 400-700 nm | 10-400 nm | 100-10^{-3} nm | 100-<10^{-3} nm |

Frequency | 30-300 Hz | 20 Hz-30 MHz | 300 MHz – 300 GHz | 300 GHz – 300 THz | 430-750 THz | 750-3000 THz | 3000 THz – 10^{20} Hz | 3000 THz to >10^{20} Hz |

Photon energy | Pico eV (10^{-12 }eV) | Nano to micro eV | Micro to Milli eV | Milli eV to eV | 1.8-3. 3 eV | 3-12 eV | KeV – MeV | KeV – >MeV |

**Σ** Summary

- Radiation is both a wave and particles
- An electromagnetic wave is sinusoidal perpendicular to time and distance
- Frequency = 1 / period (units = s
^{-1}or Hz (1 Hz = 1 cycle per second)) - Velocity = f x λ, where f = frequency and λ = wavelength
- Intensity is proportional to frequency
- Intensity is inversely proportional to wavelength
- Inverse square law: intensity inversely proportional to distance
^{2}but only if:- Beam comes from a point source
- No scatter or absorption of the beam