How this calculator works
Thermal equilibrium assigns a relative weight exp(-E/kBT) to an individual state. Taking the ratio cancels the partition function and leaves only the energy difference. This page uses the exact Boltzmann constant 1.380649e-23 J/K. For grouped levels with unequal degeneracies, multiply the returned ratio by g2/g1. Very small weights may underflow to zero; their natural logarithm is also reported.
Formula
N2/N1 = exp[-(E2 - E1)/(kB T)] for equal degeneracy; ln(N2/N1) = (E1 - E2)/(kB T).
Worked example
At 300 K, an energy gap of 4.141947e-21 J equals kBT, giving N2/N1 = exp(-1) = 0.3678794412. A gap of twice kBT gives exp(-2) = 0.1353352832.
Advertisement
Frequently asked questions
Can a ratio exceed one?
Yes. State 2 is more populated if its energy is lower, with equal degeneracy.
Is this an absolute probability?
No. Normalizing all accessible states requires their partition function.
Can both energies be negative?
Yes. Only their difference matters; the energy origin is arbitrary.