### Properties of Electromagnetic Waves

The wave theory of electromagnetic radiation was formalized in the 1800s by James Clerk Maxwell, who realized that such energy was a disturbance of time-varying electric and magnetic fields propagating through space, which fit the wave equation. He organized a series of equations (named, oddly enough,*Maxwell's equations*) to describe this wave motion.

Einstein's later work with the photoelectric effect revealed that electromagnetic waves carry quantized energy in the form of photons, but the wavelike properties remain in most circumstances and therefore a reformulation of Maxwell's equations are still used today to describe electromagnetic waves.

In electromagnetic radiation, the energy of the wave is related to both the frequency (*nu*) and wavelength (*lambda*) of the wave, in the following forms:

The table below shows the approximate wavelength, frequency, and energy ranges for different types of electromagnetic waves. An illustration of the spectrum is in the image to the right, which can be examined closer by clicking on it.E=h nu=hc/lambda

Notice that there is some overlap. For example, the terahertz waves (which are just now being studied and found to have intriguing properties) really lie just on the border of the microwave and infrared waves. Also, some depictions show an overlap between infrared & microwave, ultraviolet & x-ray, and x-ray & gamma rays, so these ranges are somewhat flexible at the boundaries. These values (except for the terahertz, which I calculated from other sources) came from NASA, so I figure they're close enough.

The Electromagnetic Spectrum |
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Wave Type | Wavelength (m) | Frequency (Hz) | Energy (J) |

Radio waves | > 0.1 | < 3 x 10^{9} | < 2 x 10^{-24} |

Microwaves | 10^{-3} - 0.1 | 3 x 10^{9} - 3 x 10 ^{11} | 2 x 10^{-24} -2 x 10 ^{-22} |

Terahertz waves | 10^{-3} -10 ^{-4} | 3 x 10^{11} -3 x 10 ^{12} | 2 x 10^{-22} -2 x 10 ^{-21} |

Infrared | 7 x 10^{-7} -10 ^{-3} | 3 x 10^{11} -4 x 10 ^{14} | 2 x 10^{-22} -3 x 10 ^{-19} |

Optical (visible light) | 4 x 10^{-7} -7 x 10 ^{-7} | 4 x 10^{14} -7.5 x 10 ^{14} | 3 x 10^{-19} -5 x 10 ^{-19} |

Ultraviolet | 10^{-8} -4 x 10 ^{-7} | 7.5 x 10^{14} -3 x 10 ^{16} | 5 x 10^{-19} -2 x 10 ^{-17} |

X-rays | 10^{-11} -10 ^{-8} | 3 x 10^{16} -3 x 10 ^{19} | 2 x 10^{-17} -2 x 10 ^{-14} |

Gamma rays | < 10^{-11} | > 3 x 10^{19} | > 2 x 10^{-14} |