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:

\( \frac{N2}{N1} \) is the Boltzmann ratio.
\( \Delta E \) is the energy difference in joules.
\( k_B \) is the Boltzmann constant (approximately \( 1.380649 \times 10^{-23} \) J/K).
\( T \) is the temperature in Kelvin.

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.