Result

Rydberg formula

\frac{1}{λ} = R (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})

Statement

The wavelength of light emitted or absorbed in a transition between hydrogen energy levels n_i and n_f.

Symbols and units

$λ$	emitted or absorbed wavelength	m
$R$	Rydberg constant	1.097×10⁷ m⁻¹
$n_{i}, n_{f}$	initial, final principal quantum number	—

When it applies

Hydrogen or hydrogen-like ions; R is the corresponding Rydberg constant for that ion.

Don't use when

Only for hydrogen or hydrogen-like ions — the Rydberg constant R must be the one corresponding to that specific ion.

Derivation

Follows directly from the energy difference between two hydrogen levels and the photon relation E = hc/λ.

\frac{1}{λ} = R (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})

Watch out for

Emission corresponds to n_i > n_f (the electron drops to a lower level, releasing a photon); absorption is the reverse.

Connects to