What is the Bohr model?

The Bohr model (1913) treats electrons as orbiting the nucleus in fixed circular orbits. Each orbit corresponds to a principal quantum number n, and the electron energy is quantized: E = −13.6 eV × Z² / n².

Why is the energy negative?

The negative sign means the electron is bound to the nucleus. Zero energy corresponds to a free (unbound) electron. More negative values indicate tighter binding — ground state (n=1) is most tightly bound.

What does Z represent?

Z is the atomic number — the number of protons in the nucleus. The Bohr model applies to hydrogen-like ions: atoms or ions with only one remaining electron, such as H (Z=1), He⁺ (Z=2), or Li²⁺ (Z=3).

What is ionization energy from level n?

It is the energy needed to completely remove the electron from that level: IE = 13.6 eV × Z² / n². For hydrogen ground state (n=1, Z=1) this is exactly 13.6 eV.

How is the photon wavelength calculated?

When an electron drops from level n to the ground state (n=1), the emitted photon energy equals the energy difference. Wavelength is then λ = hc / ΔE, where h = 6.626 × 10⁻³⁴ J·s and c = 3 × 10⁸ m/s.

Does this work for multi-electron atoms?

No. The Bohr model applies only to hydrogen-like (one-electron) systems. Multi-electron atoms require quantum mechanics including electron-electron repulsion.

Bohr Model Energy Levels Calculator

Enter atomic number Z and principal quantum number n to get the electron energy in eV and joules using the Bohr model.

Inputs

Atomic Number (Z)

H=1, He⁺=2, Li²⁺=3 … (hydrogen-like ions only)

Principal Quantum Number (n)

n = 1 is ground state; n = 2, 3, … are excited states

Quick Presets

Results

Enter values and click Calculate.

Energy Level Diagram (n = 1–6, Z = 1)

Click Calculate to update the diagram. Highlighted bar = selected level.

Summary

The Bohr model describes electron energy levels in hydrogen-like atoms using the formula E = −13.6 eV × Z² / n², where Z is the atomic number and n is the principal quantum number. This calculator applies that formula to give the electron energy in both electron volts and joules, the ionization energy from level n, and the photon wavelength emitted when the electron falls to the ground state.

How it works

Enter the atomic number Z (1 for hydrogen, 2 for He⁺, 3 for Li²⁺, etc.).
Enter the principal quantum number n (1 = ground state, 2, 3, … for excited states).
Click Calculate to apply E = −13.6 eV × Z² / n².
The result shows energy in eV and joules, plus the ionization energy from that level.
For transitions to n=1, the emitted photon wavelength is also shown.

Use cases

Check energy level answers for physics homework or exams.
Visualize how energy scales with quantum number n.
Compare energy levels across hydrogen-like ions (He⁺, Li²⁺).
Find the photon wavelength emitted by an electron dropping to ground state.
Compute ionization energy from a specific excited state.
Explore the hydrogen emission spectrum (Lyman, Balmer, Paschen series).

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu