Bohr Energy Levels
Energy of the nth hydrogen orbit.
Formula
Variables
Example
n=1 ⇒ −13.6 eV
How it works
This formula gives the allowed binding energies of an electron in the hydrogen atom, with negative sign indicating the electron is bound to the proton rather than free. It comes from Bohr’s quantized-orbit model, where only certain angular momenta are allowed; combining that quantization with Coulomb attraction produces discrete energy levels that scale as 1/n^2. As n increases, the levels get closer together and approach 0 eV, meaning the electron is less tightly bound and easier to ionize.
When to use it
Use this when calculating the energy of a specific hydrogen state, the energy gap between two levels, or the ionization energy from a given level. It is also useful in spectroscopy problems involving hydrogen emission or absorption lines.
Worked example, step by step
Find the energy of the hydrogen atom when n = 3. E_n = -13.6 / n^2 eV E_3 = -13.6 / 3^2 eV E_3 = -13.6 / 9 eV E_3 = -1.51 eV Final answer: the electron in the n = 3 level has energy about -1.51 eV.
Common mistakes to avoid
- Forgetting the negative sign and treating the level energy as positive
- Using n as if it were any real number instead of a positive integer quantum number
- Confusing the energy level with the emitted photon energy, which is the difference between two levels
Did You Know?
Bohr's model explained why atoms emit only specific colours, the barcode-like spectra that reveal a star's composition.
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