Calculate hydrogen energy levels from n or find photon wavelength, frequency, and energy for hydrogen-like ion transitions in eV, J, and nm.

Energy Level Calculator

Enter either n or E to calculate the other

Note: For hydrogen bound states, n is a positive integer (1, 2, 3, …) and the energy is negative (e.g., n=2 → E=-3.4 eV).

Energy Level Formula

The following equation is used to calculate the energy level of an electron in the hydrogen atom (Bohr model).

E = - (13.6 eV) / (n²)
  • Where E is the energy of the bound electron level (negative relative to the ionization limit at 0 eV)
  • n is the principal quantum number (n = 1, 2, 3, ...)

What is an Energy Level?

Definition:

An energy level is one of the discrete allowed energies that a system (such as an atom, molecule, or electron in an atom) can have.

How to Calculate Energy Level?

Example Problem:

The following example outlines the steps and information needed to calculate Energy Level.

First, determine the principal quantum number (n) of the electron in the hydrogen atom. For this example, n = 3.

Next, use the formula above to calculate the energy level:

E = - 1/n^2 * 13.6eV

E = - 1/3^2 * 13.6eV

E = -2.421e-19 Joules