Difference between revisions of "Detailed Balance"

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[[Radiative Processes in Astrophysics|Course Home]]
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===Short Topical Videos===
 
===Short Topical Videos===
 
* [http://youtu.be/Bg7gaJzzPN0 Detailed Balance (Aaron Parsons)]
 
* [http://youtu.be/Bg7gaJzzPN0 Detailed Balance (Aaron Parsons)]
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* [http://en.wikipedia.org/wiki/Kolmogorov%27s_criterion Kolmogorov's Criterion (Wikipedia)]
 
* [http://en.wikipedia.org/wiki/Kolmogorov%27s_criterion Kolmogorov's Criterion (Wikipedia)]
  
===Need a Review?===
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===Need to Review?===
 
* [[Einstein Coefficients]]
 
* [[Einstein Coefficients]]
  

Revision as of 16:05, 5 December 2017

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Detailed Balance

The Einstein analog:

So the Rate of Excitations is given by:

Suppose we have some distribution of relative velocities given by , where is the fraction of collisions occurring with relative velocities . Then:

where is the “collisional rate coefficient” . Then the Rate of de-excitation is given by:

We recognize now that is the rate of excitations of A using B moving at relative velocity . If we have detailed balance, then this has to be the same as the rate of de-excitation .

Where is the reduced mass . However many are created by collisional excitation, the same number are used for the reverse de-excitation. This is detailed balance.