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}{A e^{\frac{E}{k T}}} \end{array}

Where,

f is the energy distribution
E is the energy of the system
$\begin{array}{l} k = B o l t z m a n n c o n s t a n t = 1.38 \times 10^{- 23} m^{2} k g / s K^{2} \end{array}$
T is the absolute temperature in Kelvin

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:

\begin{array}{l} f (E) = \frac{1}{A e^{\frac{E}{k T}}} \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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