How this calculator works
A hydrogen-like atom has one bound electron: hydrogen, He+, Li2+ and similar ions. The Coulomb model gives energy proportional to -Z²/n², with zero at ionisation. We use hcRinf from CODATA 2018, so the nucleus is treated as infinitely heavy. Finite nuclear mass slightly changes hydrogen lines. Relativistic, fine-structure and radiative effects are omitted, especially relevant at high Z. Inverse calculations require a positive integer quantum number; arbitrary energies need not describe an allowed state.
Formula
En = -(hc Rinf) Z²/n² = -13.605693122994... eV × Z²/n². Ionisation energy from level n is -En.
Worked example
For hydrogen at n = 1 the model energy is about -13.605693123 eV. He+ at n = 2 has the same energy because Z²/n² = 1.
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Frequently asked questions
Does this work for neutral helium?
No. Neutral helium has two electrons and electron-electron interactions.
Why is the result slightly different from measured hydrogen?
This ideal model omits reduced nuclear mass, relativity and radiative corrections.
Can n be 1.5?
No. The principal quantum number is a positive integer; inverse inputs must be consistent with quantisation.