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The Rydberg formula (Rydberg-Ritz formula) is used in atomic physics for determining the full spectrum of light emission from hydrogen, later extended to be useful with any element.
A piece of the original document detailing the Rydberg formula in 1888. |
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:
| <math>n_1<math> |
<math>n_2<math> |
Name |
Converge toward |
| 1 |
<math>2 \rightarrow \infty<math> |
Lyman series |
91nm |
| 2 |
<math>3 \rightarrow \infty<math> |
Balmer series |
365nm |
| 3 |
<math>4 \rightarrow \infty<math> |
Paschen series |
821nm |
Rydberg formula for any hydrogen-like element
The formula above can be extended for use with any hydrogen-like chemical elements.
- <math>\frac{1}{\lambda_{\mathrm{vac}}} = RZ^2 \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)<math>
where
It's important to notice that this formula can be applied only to hydrogen-like chemical elements, i.e. elements with only one electron on external system of orbitals. Actually, it can only be applied to such elements as lithium, sodium, etc.; even so it can't describe all the spectrum lines of these elements.
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