Excitation temperature
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In statistical mechanics, the excitation temperature (TexScript error: No such module "Check for unknown parameters".) is defined for a population of particles via the Boltzmann factor. It satisfies
where
- nuScript error: No such module "Check for unknown parameters". is the number of particles in an upper (e.g. excited) state;
- guScript error: No such module "Check for unknown parameters". is the statistical weight of those upper-state particles;
- nlScript error: No such module "Check for unknown parameters". is the number of particles in a lower (e.g. ground) state;
- glScript error: No such module "Check for unknown parameters". is the statistical weight of those lower-state particles;
- expScript error: No such module "Check for unknown parameters". is the exponential function;
- Template:Mvar is the Boltzmann constant;
- ΔEScript error: No such module "Check for unknown parameters". is the difference in energy between the upper and lower states.
Thus the excitation temperature is the temperature at which we would expect to find a system with this ratio of level populations. However it has no actual physical meaning except when in local thermodynamic equilibrium. The excitation temperature can even be negative for a system with inverted levels (such as a maser).
In observations of the 21 cm line of hydrogen, the apparent value of the excitation temperature is often called the "spin temperature".[1]
References
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