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Electromagnetic Radiation

Electromagnetic waves:

  • these are energy waves that are produced by the oscillation or acceleration of an electric charge in a magnetic field:
    • the frequency of oscillation of a circuit containing capacitance (C) and inductance (L) is given by:
      • freq = 1/(2pi x sqrt(LC))
  • these waves have both an electric and a magnetic component
  • e-m radiation is one of the 3 ways of transferring heat (see also conduction & convection)
  • frequency x wavelength = constant = speed of light = 3 x 108 m/sec in a vacuum
  • speed in empty space is related to permittivity & permeability:
    • speed = 1 / sqrt (permittivity x permeability)
  • all types of e-m waves have in common the typical properties of wave motion, including diffraction and interference

Electromagnetic spectrum:

  • e-m radiation may be arranged in a spectrum according to its frequency or wavelength ranging from very high frequencies associated with cosmic sources through to the lowest frequencies which are propagated by commutated direct-current sources
  • gamma rays:
    • freq. 10(19 to 21)Hz
    • wavelength 10(-11 to -13)m
    • source: gamma decay of radioactive materials; nuclear fission;
  • X rays:
    • freq. 10(17 to 19)Hz
    • wavelength 10(-9 to -11)m
  • ultraviolet:
    • freq. 10(15 to 17)Hz
    • wavelength 10(-7 to -9)m
    • far UV <200nm
    • near UV 300nm
  • visible light:
    • freq. 10(14-15)Hz
    • wavelength 10(-6 to -7)m
    • violet 420nm
    • blue 470nm
    • green 530nm
    • yellow 580nm
    • orange 620nm
    • red 650nm 
    • spectral curves of the human retina cells:
      • S “blue” cones - peak 420nm with range up to 530nm
      • M “green” cones - peak 534nm with range up to 650nm
      • L “red” cones - peak 564nm (ie. yellow-green) with range up to 680nm
      • rods (which give B&W night vision) - peak 498nm with range up to 600nm - barely sensitive to red light, hence astronomers use red torches to minimise reducing the sensitivity of the rods due to exposure to bright lights.
  • infra-red:
    • freq. 10(11 to 14)Hz
    • wavelength 10(-3 to -6)m ie. ~650nm - 14nm
    • some materials are transparent for infrared but opaque to visible light eg. rubber, nickel oxide, special glasses, deep black solution of iodine in carbon disulphide, some types dark clothing
    • some materials such as greenhouse glass transmits higher infrared frequencies such as solar but block lower frequencies such as those radiated from within the greenhouse, thereby allowing trapping of heat radiation within the greenhouse
    • video camera “nightshot” mode and certain night vision goggles work by the CCD detecting radiated infrared heat from the environment and is sometimes supplemented by an infrared light source, although these tend to have only a short range from the light source (eg. 2-3m).
    • near infrared (not heat):
      • most digital cameras have a CCD sensitive to near IR light up to ~1100nm, but also have a special IR-blocking filter in front of the CCD as the IR light would otherwise degrade the image, thus sensitivity ranges are usually:
        • normal digital cameras with IR & UV blocking filter: 400nm to 750nm
        • normal digital camera with IR & UV blocking filter removed: 280nm to 1200nm, but because CCD sensitivity is reduced at the extremes, the practical range is approximately 325nm to 1100nm.
    • mid infrared (MIR): 4-6 micron - detected by MIR thermal cameras
    • far infrared (FIR): 8-14 micron  - detected by FIR thermal cameras
  • radio waves:
    • freq. 10(4 to 11)Hz
    • wavelength 10(4 to -3)m
    • microwaves:
      • short high frequency radio waves with wavelength 1mm-30cm
      • generated by special electron tubes such as the klystron & the magnetron, with built-in resonators to control the frequency or by special oscillators or solid-state devices
      • cannot pass through metal
      • high density microwaves (eg. masers) may cause burns, cataracts, neurologic damage and sterility
      • biologic hazard of low intensity microwaves is uncertain, but regulations usually place max. exposure level at 10mW/
      • microwave telegraphy operates in the 4GHz band
    • electronic digital data transmission:
      • usually 2.4GHz, 3GHz or 5GHz
    • radio & TV broadcasting:
      • signals are sent by modulating a carrier radio wave with a series of frequencies called sidebands that correspond to the difference and sum of the carrier frequency & the modulating frequency
      • the higher the frequency the carrier wave is, the greater the bandwidth available, but the shorter the distance it travels and it starts to behave more like light, requiring more direct line-of-sight transmission and can be reflected from hills or buildings creating multiple images, thus a standard radio station can transmit ~160km but a TV station can only transmit up to 50km
      • to minimise multiple images, antennae need to have high efficiency for one direction and low efficiency for other directions and it should have a high gain to amplify weak signals so that one can direct it at a reflected wave and exclude other reflections.
      • transmitting standard TV requires a bandwidth of ~4MHz, and thus higher frequency radio waves are used to carrier it:
        • very-high frequency (VHF): 54-216 MHz
        • ultra-high frequency (UHF): 470-806 MHz
      • transmitting AM radio requires a bandwidth of ~10kHz, thus stations only need to be 10kHz apart to avoid interference
        • FM radio: 88-107MHz
        • Short wave radio 2.3 - 22MHz:
        • AM radio: 500-1500kHz
  • electric waves:
    • freq. 10-1 to 4Hz
    • wavelength 107 to 4m

Heat radiation:


  • all bodies emit radiant energy, they do so in the form of electromagnetic radiation as a result of the oscillations of its atoms
  • when radiant heat is absorbed by a body, its atoms are excited and oscillate faster, converting the radiant energy into kinetic energy
  • heat radiation consists of infra-red waves
  • the ideal radiator is a “blackbody”, which is also the ideal absorber of radiated heat
    • thus black objects both absorb & radiate heat the best, but reflect heat the poorest and the converse is true for highly reflective surfaces


how much heat is radiated?

  • radiancy is the rate at which energy is radiated per unit area of the object
  • for an ideal blackbody, the Stefan-Boltzmann law determines the total energy of all wavelengths radiated from a body at a given temperature:
    • power (watts) = 5.70×10(-12) x area in x (temperature in Kelvin)4
  • for non-ideal blackbodies, the power can be determined by multiplying the blackbody calculated power by the body's total emissivity of the surface which is the ratio of the radiancy of that surface to the radiancy of a blackbody at the same temperature

what is the rate of change in temperature of the body due to radiation of heat?

  • as the body will lose heat that it radiates, it will simultaneously gain heat from absorbed radiation from its surroundings, thus the rate of temperature change in a blackbody due to radiation can be calculated by:
    • rate of heat energy change (watts) = 5.70×10(-12) x area in x ((temp. of body K)4 - (temp. of surround K)4)
    • NB. 1 watt = 1 joule/sec and 1 joule = 1 newton-meter and will raise the temperature of 1ml of water by 1 deg. Celsius
  • for small relative differences in temperature in degrees K, however, there is no need to raise the power to 4, as this will give a good approximation for rate of heat exchange, thus, to take into account exchanges due to conduction and convection as well, the Newton's law of cooling approximation can be used:
    • rate of heat energy change = constant for object x area in x ((temp. of body K) - (temp. of surround K))

which wavelengths are radiated?

  • a body radiates heat in various frequencies of e-m radiation, and its peak frequency becomes higher in proportion to the temperature of the body and can be calculated from Wien's displacement law:
    • peak wavelength radiated in microns = 2897.2/(temperature in Kelvin)
  • as atoms can only have certain energy levels, radiation obeys the laws of quantum physics, thus the spectral radiancy (ie. the radiancy for a given radiated wavelength) of an object can be determined from Planck's law:
    • radiancy for given wavelength radiated = 2 x pi x h x f5 /(c3 x (e(hf/kT) - 1)), where:
      • h = Planck's constant = 6.62 x 10(-34) joule-sec
      • f = frequency in Hz
      • c = speed of light
      • k = Boltzmann constant
      • T = temperature in Kelvin
  • for non-ideal blackbodies, the above should be multiplied by the body's spectral emissivity which is analogous to its total emissivity except it is the ratio of spectral radiancy rather than radiancy


Cosmic Rays:

  • cosmic rays:
    • cosmic rays were discovered in 1912 by Victor Hess, when he found that an electroscope discharged more rapidly as he ascended in a balloon. He attributed this to a source of radiation entering the atmosphere from above, and in 1936 was awarded the Nobel prize for his discovery. 
    • For some time it was believed that the radiation was electromagnetic in nature (hence the name cosmic “rays”), and some textbooks still incorrectly include cosmic rays as part of the electromagnetic spectrum.
    • source: the Big Bang - the cosmic background radiation is the leftover from the matter-antimatter annihilations
    • Cosmic rays from outer space were the first high energy particles ever studied. From the 1930s to the 1950s, before man-made particle accelerators reached very high energies, cosmic rays served as a source of particles for high energy physics investigations, and led to the discovery of subatomic particles that included the positron and muon.
    • They gave a tantalizing glimpse of the subatomic world before accelerators were invented. A few cosmic rays pass through your body every second of every day, no matter where you are.
    • It is difficult to work out the exact origin of cosmic rays because they are arriving from all directions. Many were probably thrown into space by supernovae, the huge explosions of dying stars.
    • The energy of cosmic rays is usually measured in units of MeV, for mega-electron volts, or GeV, for giga-electron volts. (One electron volt is the energy gained when an electron is accelerated through a potential difference of 1 volt). Most galactic cosmic rays have energies between 100 MeV (corresponding to a velocity for protons of 43% of the speed of light) and 10 GeV (corresponding to 99.6% of the speed of light). The number of cosmic rays with energies beyond 1 GeV decreases by about a factor of 50 for every factor of 10 increase in energy.
    • It is believed that most galactic cosmic rays derive their energy from supernova explosions, which occur approximately once every 50 years in our Galaxy.
    • Because cosmic rays are electrically charged they are deflected by magnetic fields, and their directions have been randomized, making it impossible to tell where they originated.
    • When high energy cosmic rays undergo collisions with atoms of the upper atmosphere, they produce a cascade of “secondary” particles that shower down through the atmosphere to the Earth's surface. Secondary cosmic rays include pions (which quickly decay to produce muons, neutrinos and gamma rays), as well as electrons and positrons produced by muon decay and gamma ray interactions with atmospheric atoms. The number of particles reaching the Earth's surface is related to the energy of the cosmic ray that struck the upper atmosphere.
    • Most secondary cosmic rays reaching the Earth's surface are muons, with an average intensity of about 100 per m2 per second. Although thousands of cosmic rays pass through our bodies every minute, the resulting radiation levels are relatively low, corresponding, at sea level, to only a few percent of the natural background radiation. However, the greater intensity of cosmic rays in outer space is a potential radiation hazard for astronauts, especially when the Sun is active, and interplanetary space may suddenly be filled with solar energetic particles. Cosmic rays are also a hazard to electronic instrumentation in space; impacts of heavily-ionizing cosmic ray nuclei can cause computer memory bits to “flip” or small microcircuits to fail.
    • Cosmic rays hitting the outer atmosphere are mainly fast-moving, high-energy protons. As they hurtle towards the Earth, they collide with atoms in the air. Some of the collision energy reappears as the mass of new pairs of particles and antiparticles, following Einstein's famous equation E=mc2.
    • Cosmic rays are thus a natural source of antiparticles - and in 1932 Carl Anderson's studies of cosmic rays revealed the first antiparticle ever seen, the antielectron, or “positron”.
photo/p_emrad1.txt · Last modified: 2012/04/05 11:20 by gary1

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