What is the Rydberg formula?

1/λ = R(1/n_f² − 1/n_i²), where R ≈ 1.097 × 10⁷ /m. It predicts the wavelengths of spectral lines emitted when an electron in a hydrogen atom drops from level n_i to n_f.

What are the spectral series?

Lyman (n_f = 1, UV), Balmer (n_f = 2, visible), Paschen (n_f = 3, IR), Brackett (n_f = 4, IR), and Pfund (n_f = 5, IR).

What is the Bohr energy level?

E_n = −13.6/n² eV. The ground state is n = 1 with E₁ = −13.6 eV; ionisation from the ground state requires 13.6 eV.

What does the calculator return?

Wavelength of the photon, frequency, photon energy, the series name (Lyman/Balmer/etc.), and the initial and final Bohr energies.

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NSW · HSCModule 8

Rydberg / hydrogen spectrum calculator

Predict the wavelength of any hydrogen spectral line from the Bohr levels n_i and n_f.

Inputs

Final level n_fFor emission, the lower levelInitial level n_i

R = 1.097 × 10⁷ /m. Bohr energy: E_n = -13.6/n² eV.

Result

Wavelength λ

656.3nm

Frequency f

4.568e+14Hz

Photon energy

1.889eV

Series

Balmer (visible/UV)

E_i

-1.511eV

E_f

-3.400eV

1/λ = R(1/n_f² − 1/n_i²). The Balmer series (n_f = 2) is the visible hydrogen spectrum.

How this calculator works

The Rydberg formula 1/λ = R(1/n_f² − 1/n_i²) gives the wavelength in inverse metres. The calculator inverts to get λ, then uses c = fλ and E = hf to compute frequency and photon energy. It also labels the series for you.

Common questions

What is the Rydberg formula?: 1/λ = R(1/n_f² − 1/n_i²), where R ≈ 1.097 × 10⁷ /m. It predicts the wavelengths of spectral lines emitted when an electron in a hydrogen atom drops from level n_i to n_f.
What are the spectral series?: Lyman (n_f = 1, UV), Balmer (n_f = 2, visible), Paschen (n_f = 3, IR), Brackett (n_f = 4, IR), and Pfund (n_f = 5, IR).
What is the Bohr energy level?: E_n = −13.6/n² eV. The ground state is n = 1 with E₁ = −13.6 eV; ionisation from the ground state requires 13.6 eV.
What does the calculator return?: Wavelength of the photon, frequency, photon energy, the series name (Lyman/Balmer/etc.), and the initial and final Bohr energies.