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Boltzmann Ratio Calculator

Formula

The formula to calculate the Boltzmann Ratio (N2/N1) is:

$\frac{N2}{N1} = e^{\left(-\frac{\Delta E}{k_B \cdot T}\right)}$

Where:

Boltzmann Ratio: The relative population of particles in different energy states at thermal equilibrium.
Energy Difference (ΔE): The difference in energy between two states, measured in joules.
Boltzmann Constant (kB): A physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas, approximately $1.380649 \times 10^{-23}$ J/K.
Temperature (T): The measure of the thermal energy of a system, measured in Kelvin.

Let's say the energy difference is $2 \times 10^{-21}$ Joules and the temperature is 300 Kelvin. Using the formula:

$\frac{N2}{N1} = e^{\left(-\frac{2 \times 10^{-21}}{1.380649 \times 10^{-23} \cdot 300}\right)}$

We get:

$\frac{N2}{N1} \approx 0.617$

So, the Boltzmann Ratio ( $\frac{N2}{N1}$ ) is approximately 0.617.