Rydberg formula

The spectrum are the wavelengths of photons emitted when electrons jump between discrete energy levels, "shells" around the atom of a certain chemical element.

The fomula was invented by the Swedish physicist Janne Rydberg and presented on November 5, 1888.

Rydberg formula for hydrogen

<math>\frac{1}{\lambda_{\mathrm{vac}}} = R_{\mathrm{H}} \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)</math>

Where

• <math>\lambda_{\mathrm{vac}}</math> is the wavelength of the light emitted in vacuum.
• <math>R</math> is the Rydberg constant for hydrogen.
• <math>n_1</math> and <math>n_2</math> are integers such that <math>n_1 < n_2</math>.

By setting <math>n_1</math> to 1 and letting <math>n_2</math> run from 2 to infinity, the spectral lines known as the Lyman series[?] converging to 91nm are obtained, in the same manner:

Rydberg formula for any element

The formula above can be extended for use with any chemical element.

<math>\frac{1}{\lambda_{\mathrm{vac}}} = RZ^2 \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)</math>

Where

• <math>\lambda_{\mathrm{vac}}</math> is the wavelength of the light emitted in vacuum
• <math>R</math> is the Rydberg constant for this element.
• <math>Z</math> is the atomic number i.e. number of protons in the atomic nucleus of this element.
• <math>n_1</math> and <math>n_2</math> are integers such that <math>n_1 < n_2</math>.