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.