The Bohr model energy calculator computes hydrogen atom electron energy levels, photon wavelengths emitted or absorbed during transitions, and identifies the spectral series (Lyman, Balmer, Paschen). Based on Bohr's quantized orbit model from 1913.
Hydrogen Energy Level Calculator
Calculation Type
Result
Step-by-Step
Spectral Series Reference
| Series | Final n | Region | Wavelengths |
|---|---|---|---|
| Lyman | n=1 | Ultraviolet | 91–121 nm |
| Balmer | n=2 | Visible / UV | 365–656 nm |
| Paschen | n=3 | Infrared | 820–1876 nm |
| Brackett | n=4 | Infrared | 1458–4051 nm |
How to Use the Bohr Model Energy Calculator
The Bohr model quantizes hydrogen atom energy levels as E_n = −13.6/n² eV. Transitions between levels release or absorb photons with energy equal to the difference between levels.
Single Level Mode
Enter a principal quantum number n (1–20) to see the electron's energy at that level. The ground state (n=1) has E = −13.6 eV. Higher n values approach 0 eV (ionization).
Transition Mode
Enter the initial level (higher n) and final level (lower n) for emission. The photon energy is ΔE = 13.6 × (1/n_f² − 1/n_i²) eV. Wavelength = 1240/ΔE(eV) nm.
Example: Hydrogen H-alpha Line
The n=3 → n=2 Balmer transition: ΔE = 13.6 × (1/4 − 1/9) = 13.6 × 5/36 = 1.889 eV. Wavelength = 1240/1.889 = 656.7 nm — the famous red Hα line visible in hydrogen emission spectra.
Spectral Series
The Lyman series (all transitions to n=1) is in ultraviolet. The Balmer series (to n=2) includes the visible lines. The Paschen series (to n=3) is in near-infrared. These series are how astronomers identify hydrogen in stars.
FAQ
What is the Bohr model?
The Bohr model (1913) describes the hydrogen atom as an electron orbiting a proton in discrete energy levels. Electrons can only occupy specific orbits (n=1, 2, 3...) and emit or absorb photons when transitioning between levels. The energy of level n is E_n = -13.6/n² eV.
What are the hydrogen spectral series?
The Lyman series (n=2,3,4... → n=1) produces ultraviolet light. The Balmer series (n=3,4,5... → n=2) produces visible light (H-alpha at 656nm is red). The Paschen series (n=4,5,6... → n=3) produces infrared light.
How do I calculate photon energy from a transition?
The energy released or absorbed is ΔE = 13.6 × (1/n_lower² - 1/n_upper²) eV. To find the photon wavelength: λ = hc/ΔE, where h = 4.136×10⁻¹⁵ eV·s and c = 3×10⁸ m/s.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
What is the ground state energy of hydrogen?
The ground state (n=1) energy is -13.6 eV. The negative sign indicates the electron is bound to the nucleus. To ionize hydrogen (remove the electron completely) requires 13.6 eV of energy.