Quantum Energy Levels Calculator

Calculate atomic energy levels, transition energies, photon wavelengths, and spectral series for hydrogen-like atoms.

Atomic Number (Z)

Initial Level (n)

Target Level

Tab to move between fields

Energy at n

-13.6 eV

Transition Energy

10.2 eV

Photon Wavelength

121.57 nm

Ionization Energy13.6 eV

Orbital Radius0.529 A

Degeneracy (2n²)2

How to Use This Calculator

Enter Atomic Number (Z): 1 for hydrogen, 2 for helium (hydrogen-like), up to heavy elements for single-electron ions.
Enter Initial Level (n) — the principal quantum number of the starting energy level (n = 1 is the ground state).
Enter Target Level for the transition you want to analyze — higher target means lower-energy photon emitted.
Read Energy at n (eV), Transition Energy (eV), and Photon Wavelength (nm) to identify the spectral line.
Compare Photon Wavelength to known series: Lyman (UV, <400 nm), Balmer (visible, 400–700 nm), Paschen (IR, >700 nm).

What each input means

Eₙ = -13.6 eV × Z² / n²

Identify Input Parameters
Atomic Number (Z) = 1, Initial Level (n) = 1, Target Level = 2 = 3 input(s) provided
Calculate Energy at n
Energy at n
-13.6 = -13.6
Calculate Transition Energy
Transition Energy
10.2 = 10.2
Calculate Photon Wavelength
Photon Wavelength
121.57 = 121.57
Calculate Ionization Energy
Ionization Energy
13.6 = 13.6
Calculate Orbital Radius
Orbital Radius
0.529 = 0.529

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