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 Distance

Graph Showing Wave Strength Over Time

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.

E = hf

Key:

E = photon energy\ 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)

Definitions

Diagram representing a beam emanating from a point source

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/mm2) (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.

A ∝ d2

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 / d2

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 100-10-3nm 100-<10-3nm
Frequency 30-300 Hz 20 Hz-30 MHz 300 MHz - 300 GHz 300 GHz - 300 THz 430-750 THz 750-3000 THz 3000 THz - 1020Hz 3000 THz to >1020 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

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 distance2 but only if:
    • Beam comes from a point source
    • No scatter or absorption of the beam