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Bohr Model Calculator

Calculate the electron orbit radius and energy level for a hydrogen-like atom using Niels Bohr’s model of the atom.

What the Bohr model describes

The Bohr model treats electrons in a hydrogen-like atom (one electron orbiting a nucleus) as occupying fixed circular orbits with quantized energy levels, identified by the principal quantum number n.

The formulas

Orbital radius: r = a0 × n² / Z, where a0 is the Bohr radius (5.29177210903 × 10⁻¹¹ m) and Z is the atomic number. Energy level: E = -13.6057 × Z² / n² electron-volts, matching the hydrogen spectrum when Z = 1.

The Bohr model is a simplified, historically important approximation; modern quantum mechanics gives a more complete picture, but this model remains a useful teaching tool for hydrogen-like systems.

Last reviewed August 2026