Maxwell Boltzmann Formula

Maxwell Boltzmann Formula clearly describes the distribution of energy between identical particles but which are distinguishable.

Formula of Maxwell Boltzmann

\(\begin{array}{l}f(E)=\frac{1}{Ae^{\frac{E}{kT}}}\end{array} \)


  • f is the energy distribution
  • E is the energy of the system
  • \(\begin{array}{l}k\,=\,Boltzmann\,constant\,=\,1.38\times 10^{-23}m^{2}kg/sK^{2}\end{array} \)
  • T is the absolute temperature in Kelvin

Solved Example

Example 1:

Calculate the Maxwell Boltzmann for a blackbody whose temperature is 5000000 K. Also, determine if the distribution is larger or shorter.


The Maxwell Boltzmann formula is:

\(\begin{array}{l}f(E)=\frac{1}{Ae^{\frac{E}{kT}}}\end{array} \)

Substituting the values we get,

f = 0.9998

Also, there is a rise in the temperature therefore the distribution is larger.

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