Bohr Energy Levels

In-depth explanation of Bohr Energy Levels

For a hydrogen-like ion the energy of level n is E_n = -13.6 eV x Z^2 / n^2. Energies are negative because the electron is bound, and zero energy corresponds to a free electron at rest at infinity. Levels crowd closer together as n increases, approaching the ionisation limit. The ionisation energy of hydrogen is 13.6 eV, the energy needed to remove its electron from n = 1. Transitions between levels produce photons whose energies match the observed spectral lines.

Going deeper: Bohr Energy Levels

Key ideas: E_n = -13.6 eV x Z^2 / n^2 = -2.18 x 10^-18 J x Z^2 / n^2, with radius r_n = 52.9 pm x n^2 / Z. Ground state of H is -13.6 eV, ionization energy is +13.6 eV. Transition energy: delta E = 13.6 x Z^2 (1 / n1^2 - 1 / n2^2) eV. Velocity falls as 1 / n.

Common mistakes and connections: Students drop the negative sign: bound energies are negative, zero at infinite separation, so higher levels are less negative. Another error is forgetting Z^2 for He+ (E_1 = -54.4 eV). Levels crowd closer as n increases. This connects to the Rydberg equation and ionization energy.

Visualization of Bohr Energy Levels

For He+ the Bohr energies are -13.6 eV times Z^2 over n^2, four times deeper than hydrogen's levels with Z squared equal to 4. The interactive lesson shows this as a live animation or chart.

Worked example and use case

The n = 2 level of hydrogen lies at -3.4 eV, so a photon of 10.2 eV can excite an electron from n = 1 to n = 2.

Where Bohr Energy Levels fits in Atomic Structure & Periodicity

Bohr Energy Levels is topic 46 of 115 in Atomic Structure & Periodicity.

Related topics

• Hydrogen Spectrum SeriesIntermediate
• Rydberg EquationIntermediate
• Bohr ModelIntermediate
• Limitations of Bohr ModelIntermediate
• de Broglie HypothesisIntermediate
• Heisenberg Uncertainty PrincipleIntermediate

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