Quantum Number Calculator

Bohr model results for hydrogen: energy Eₙ and radius rₙ.

How to Use This Calculator

1

Enter integer n

Use n = 1, 2, 3, … Higher n have higher energy (less negative) and larger radius.

Formula

Eₙ = −13.6 eV / n²,   rₙ = a₀ n²

a₀ ≈ 0.529 Å. This is the simple Bohr model for hydrogen (Z = 1).

Frequently Asked Questions

Does this work for hydrogen-like ions?

For Z > 1, Eₙ = −13.6 Z² / n² eV and rₙ = a₀ n² / Z. This tool assumes Z = 1.

How accurate is the Bohr model?

It’s a historical model. Quantum mechanics (Schrödinger) gives exact hydrogen energies but agrees on Eₙ ∝ 1/n².