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## Doppler broadening
## Additional recommended knowledgeThe Doppler profile in wavelength is a normal distribution with a standard deviation of where λ where ## Derivation of Doppler profileWhen thermal motion causes a particle to move towards the observer, the emitted radiation will be shifted to a higher frequency. Likewise, when the emitter moves away, the frequency will be lowered. For non-relativistic thermal velocities, the Doppler shift in frequency will be: where Since there is a distribution of speeds both toward and away from the observer in any volume element of gas, the net effect will be to broaden the observed line. The distribution of speeds towards and away from an observer is given by the Maxwell distribution. If where In optics we measure frequency content (as opposed to velocity content), and it is convenient to re-express the distribution in terms of The Doppler shift equation can be used to express velocity in terms of the frequency. Using the relationship from probability that We can simplify this expression as: - ,
which we immediately recognize as a Gaussian peak with standard deviation and full width at half maximum We can also consider the above equation in terms of wavelength - .
and furthermore apply the change of variable with standard deviation and full width at half maximum ## Nuclear technology
In a nuclear reactor, this effect reduces the power generated as the reactor temperature increases. When a reactor gets hotter, the accelerated motion of the atoms in the fuel increases the probability of neutron capture by U-238 atoms. When the uranium is heated, its nuclei move more rapidly in random directions, and therefore see and generate a wider range of relative neutron speeds. U-238, which forms the bulk of the uranium in the reactor, is much more likely to absorb fast neutrons.[1] This reduces the number of neutrons available to cause U-235 fission, reducing the power output by the reactor. In some reactor designs, such as the pebble bed reactor, this natural negative feedback places an inherent upper limit on the temperature at which the chain reaction can proceed. Such reactors are said to be "inherently safe" because a reactor failure cannot generate a criticality excursion. It is worth noting, however, that because of decay heat emitted from the decay of fission products, a meltdown is still theoretically possible if the ability to cool the reactor is lost, and thus the reactor design must be designed to prevent loss of coolant accident. ## AstronomyIn Astronomy, Doppler broadening is one of the explanations for the broadening of spectral lines, and as such gives an indication for the relative temperatures of observed material. There are, however many other factors which can broaden the lines as well. For example high surface gravity (a sign of small stars) leads to high pressure, which in turn leads to Stark-broadening (see Spectral line). |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Doppler_broadening". A list of authors is available in Wikipedia. |