Razão Boltzmann N2/N1
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Boltzmann population ratio calculator determines the proportion between two energy levels in systems at thermal equilibrium using N2/N1 = exp(−ΔE/kT). ΔE is the energy difference, k is Boltzmann's constant, and T is absolute temperature.
It's used in statistical physics to model particle distributions in gases, solids, or chemical reactions. For lasers, it calculates population inversion needed for coherent emission. The formula assumes thermal equilibrium and Kelvin temperature.
Notes: Use ΔE in joules or eV matching the k unit. Negative ΔE flips the ratio (N1/N2). For non-equilibrium systems, results are approximations.
Frequently asked questions
Why does the ratio decrease with temperature?
Higher temperature increases kT in the denominator, reducing the exponential term. At higher temperatures, higher energy levels become more populated.
What if ΔE is negative?
The ratio inverts to N1/N2 because the ΔE sign changes. This means the lower energy level is more populated.
Can it be used in non-quantum systems?
Yes, if energy levels are well-defined and the system is in thermal equilibrium, like chemical reactions or gases.
What affects accuracy?
Thermal equilibrium assumptions and correct measurement of ΔE and T. Non-ideal systems may show deviations.