About the Bohr Model
Niels Bohr's 1913 model of the atom treats an electron as orbiting the nucleus only in fixed, quantized energy levels labeled by a principal quantum number n = 1, 2, 3, ... An electron can jump between two levels by absorbing a photon (moving up) or emitting a photon (moving down), and the photon's energy exactly equals the difference between the two levels' energies. This calculator applies that model to a hydrogen-like atom — a nucleus of atomic number Z with a single orbiting electron, such as hydrogen (Z=1), He+ (Z=2), or Li2+ (Z=3).
Understanding the formula
The energy of an electron in level n of a hydrogen-like atom is E(n) = -13.6 eV × Z² / n², where 13.6 eV is the Rydberg energy (hydrogen's ionization energy) and the minus sign shows the electron is bound to the nucleus. For a transition between an initial level n1 and a final level n2, the photon energy is ΔE = |E(n2) - E(n1)|. That energy converts to a wavelength via λ = h·c / ΔE (Planck's constant h and the speed of light c) and to a frequency via f = ΔE / h = c / λ.
Reading the direction and series
- If n1 is greater than n2, the electron falls to a lower level and a photon is emitted; if n1 is less than n2, a photon must be absorbed to push the electron up.
- Transitions that end on n=1 form the Lyman series (ultraviolet), those ending on n=2 form the Balmer series (visible and near-UV, including the famous red Hα line), and those ending on n=3 form the Paschen series (infrared).
- Always include units in your answer — a wavelength without nm or a frequency without Hz is not meaningful.
Knowing the limits
The Bohr model is exact only for one-electron systems (hydrogen and hydrogen-like ions); it does not correctly predict energy levels for multi-electron atoms because it ignores electron-electron repulsion and orbital shape (s, p, d, f) effects captured by full quantum mechanics. It also omits fine-structure and relativistic corrections, which shift real spectral lines by a small amount. For hydrogen and hydrogen-like ions, though, the energy levels it predicts match measured spectra closely.
Frequently Asked Questions
What is the Bohr model formula for energy levels?
How do you find the wavelength of a spectral line?
What are the Lyman, Balmer, and Paschen series?
Does the Bohr model work for atoms other than hydrogen?
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| Category | % of Net Income | Examples |
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Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |