Bohr Model Calculator

Hydrogen Energy Levels in the Bohr Model

The Bohr model quantizes electron orbits in hydrogen-like atoms. Each level has a negative energy and a characteristic orbital radius. Transitions between levels emit or absorb photons whose wavelength follows from the energy difference.

Bohr Model Equations

$$ E_n = -\frac{13.6}{n^2}\,\mathrm{eV} \qquad r_n = n^2 \times 0.529\,\mathrm{\AA} $$ $$ \Delta E = E_{n_i} - E_{n_f} = \frac{hc}{\lambda} $$

The n=2 to n=1 transition (Lyman-alpha series member for n=2→1 is actually Balmer if from higher... 2→1 is Lyman-alpha at 121.6 nm) releases 10.2 eV. Related: Bragg's Law Calculator and Beat Frequency Calculator.

Frequently Asked Questions

What is the ground state energy of hydrogen?

E₁ = -13.6 eV. Higher n values are less negative, so they have more energy.

What wavelength is emitted for n=2 to n=1?

About 121.6 nm in the ultraviolet (Lyman-alpha). ΔE = 10.2 eV.

What is the Bohr radius?

For n=1, r₁ = 0.529 Å, the standard Bohr radius a₀.

Does this work for helium?

Only hydrogen-like atoms with one electron are described accurately by this simple Bohr formula.

Why are energy levels negative?

Zero energy is defined at infinite separation. Bound states have less energy than free electrons, so they are negative.

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Hydrogen Energy Levels in the Bohr Model

Bohr Model Equations

Frequently Asked Questions

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