Skip to main content
⚛️

Bohr Energy Calculator

Featured

Use our bohr energy calculator for quick and accurate calculations. Free online tool.

🌈 Spectroscopy Energy 🌍 Available in 12 languages

Calculator

Bohr Model Energy Calculator

En = -13.6/n² eV

About the Bohr Model Energy Calculator

The Bohr Model Energy Calculator computes the energy of an electron in the nth orbit of a hydrogen-like atom using the Bohr model formula. It is ideal for students and researchers studying atomic structure, spectroscopy, and quantum mechanics. The tool instantly returns the energy in electronvolts (eV) or joules for any principal quantum number n.

The Bohr energy formula for hydrogen is En = -13.6 / n² eV. For n = 1 (ground state) E1 = -13.6 eV; for n = 2, E2 = -3.4 eV; for n = 3, E3 = -1.51 eV. The negative sign indicates a bound state. The energy difference between two levels, for example n = 2 to n = 1, is delta-E = -3.4 - (-13.6) = 10.2 eV, corresponding to the Lyman-alpha photon at 121.6 nm.

Enter the principal quantum number n (integer >= 1) and optionally the atomic number Z for hydrogen-like ions (En = -13.6 Z²/n² eV). Outputs include energy in eV and joules. Applications: calculating spectral line positions, verifying ionization energies, and understanding electron shell structure in introductory quantum chemistry.

Frequently Asked Questions

What is the Bohr model?

The Bohr model describes the hydrogen atom as an electron orbiting a nucleus in discrete, quantized orbits with specific energies, explaining why atoms emit light at specific wavelengths.

What is the ground state energy of hydrogen?

The ground state energy (n = 1) of hydrogen is -13.6 eV, meaning 13.6 eV of energy is needed to completely ionize the atom from its lowest energy state.

Does the Bohr model work for all atoms?

The Bohr model is accurate only for hydrogen and hydrogen-like ions (one electron), such as He+, Li2+. For multi-electron atoms, quantum mechanical models are required.

What happens when n approaches infinity?

As n approaches infinity, En approaches 0 eV, meaning the electron is completely separated from the nucleus and the atom is ionized.

How do I convert Bohr energies to joules?

Multiply eV by 1.602 x 10^-19 J/eV; for example, -13.6 eV = -13.6 x 1.602 x 10^-19 = -2.179 x 10^-18 J.