Maxwell-Boltzmann Distribution Formula

The Maxwell-Boltzmann distribution is the classical function for a distribution of an amount of energy between identical but distinguishable particles. It gives information about the occurrence of a particle at a given temperature and a given energy.

Maxwell-Boltzmann distribution = 1 / Exponential^{(energy/(Boltzmann constant Temperature))}

The equation is:

f= 1/exp(-E/kT)

Where:

f: Energy distribution

E: energy of the system

k: Boltzmann constant. (1.38*10^(-23) m² kg /(s K²))

T: Absolute Temperature in Kelvin.

Maxwell-Boltzmann distribution Formula Questions:

1) If the temperature of a black body radiator is 5000 K, at an energy of 1*10^(-19) J , which is its value of the distribution at that state?

Answer:

The distribution is found with the formula:

f = 1/exp(-E/kT)

then,

f = 1/exp(-1*10^(-19) J/(1.38*10^(-23) m² Kg/(s K²)*5000 K)) = 0.234

2) The same black body before, but at temperature of 5000000 K, what is the value of the distribution, larger or shorter?

Answer:

The distribution is found with the formula:

f = 1/exp(E/kT)

then,

f = 1/exp(1*10^(-19) J/(1.38*10^(-23) m² Kg/(s K²)*5000000 K)) = 0.9998

As temperature rises, the occurrence is larger.