# Maxwell Boltzmann Formula

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

## Formula of Maxwell Boltzmann

$$f(E)=\frac{1}{Ae^{\frac{E}{kT}}}$$

Where,

• f is the energy distribution
• E is the energy of the system
• $$k\,=\,Boltzmann\,constant\,=\,1.38\times 10^{-23}m^{2}kg/sK^{2}$$
• 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.

Solution:

The Maxwell Boltzmann formula is:

$$f(E)=\frac{1}{Ae^{\frac{E}{kT}}}$$

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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