Electromagnetic radiation
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 pointing at right angles to one another and to the direction of the travel of the wave.
Graph Showing Wave Strength Over Distance
Graph Showing Wave Strength Over Time
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 distance travelled 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 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.
h = Planck's constant
f = frequency
Rearranging the earlier equation of velocity = fλ and assuming that the velocity if 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)
Now available as an eBook to download and read anytime!
Witten by radiologists, for radiologists with over 220 beautiful diagrams optimised for Amazon Kindle. The proceeds of this book will help us to maintain the Radiology Cafe website.
Definitions
The diagram represents a beam emanating from a point source (S). As the beam moves further from the source it spreads (area B is larger than area A).
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 different 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 the distance squared.
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 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 coming 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 | 400-100 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 3V | 3-12 eV | KeV - MeV | KeV - >MeV |
- 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