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Bohr Model Energy Levels Calculator

Work out bohr model energy levels instantly with clear inputs, formula shown and shareable results.

About Bohr Model Energy Levels Calculator

The Bohr model gives hydrogen-like energy levels as -13.606 Z^2/n^2 eV. Hydrogen's ground state is -13.606 eV, and the n = 2 level sits at -3.401 eV, so 3.4 eV ionises an excited atom against 13.6 eV for the ground state. Orbit radius grows as n^2 and shrinks with Z, which is why heavy ions are so compact.

Formulas

Energy levels

E(n) = -13.606 Z^2 / n^2 eV

Orbit radius

r(n) = 0.0529 n^2 / Z nm

Worked example

With the default values below, Bohr Model Energy Levels Calculator returns Energy Of That Level of -3.4014. Change any input above and every figure here is recalculated in your browser.

Inputs used

Principal quantum number naccepts 1–100
2
Nuclear charge Zminimum 1
1

Results

Energy Of That Level
-3.4014 eV
Energy Needed To Remove The Electron
3.4014 eV
Bohr Orbit Radius
0.21167 nm
Electron Orbital Speed
1.0939 × 10⁶ m/s

Step by step

  1. 1Values used
  2. 2Energy levels
  3. 3Orbit radius
  4. 4Energy Of That Level= -3.4014 eV
  5. 5Energy Needed To Remove The Electron= 3.4014 eV
  6. 6Bohr Orbit Radius= 0.21167 nm
  7. 7Electron Orbital Speed= 1,093,850.0000 m/s

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why are the energies negative?

Because a bound electron sits below the free-electron zero. The magnitude is the energy needed to liberate it.

Does the Bohr model work for other atoms?

Only for one-electron systems - hydrogen, He+, Li2+ and so on. Multi-electron atoms need quantum mechanics with electron repulsion.

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