Bohr Model Energy Calculator

About this calculator

This calculator finds the energy of an electron orbit in a hydrogen-like atom (one electron orbiting a nucleus of charge Z) using the Bohr model formula E_n = −13.6·Z²/n² electron-volts, where n is the principal quantum number (1, 2, 3…) labeling the orbit and Z is the atomic number. Proposed by Niels Bohr in 1913, the model quantizes electron orbits into discrete allowed energy levels, and the energy differences between levels correspond exactly to the wavelengths of light absorbed or emitted when an electron jumps between them — explaining the discrete spectral lines of hydrogen's Lyman, Balmer, and Paschen series.

Chemistry and physics students use this as the standard first model for understanding atomic structure and quantized energy, before moving on to the full quantum mechanical treatment; and it remains a useful teaching and estimation tool for atomic emission spectra even though later quantum mechanics superseded it as a complete description. Enter the atomic number and quantum level to get the orbital energy.