Rydberg formula
The Rydberg formula (also Rydberg-Ritz formula ) is used in atomic physics to determine the line spectrum of the light emitted by hydrogen . It shows that the binding energy of the electron in the hydrogen atom is inversely proportional to the square of the principal quantum number .
The formula was presented on November 5, 1888 by the Swedish physicist Johannes Rydberg ; and Walter Ritz was working on her.
Corrections due to angular momentum or relativistic effects are not taken into account in the Rydberg formula . It was later expanded to determine the spectrum of other elements (see extensions below).
Rydberg's formula for hydrogen
formulation
Are there
- the wavelength of light in a vacuum
-
the Rydberg constant for the respective element : with
- the mass of the electron
- the nuclear mass (depending on the isotope present )
- the Rydberg constant for infinite nuclear mass. There
- and integer values of the main quantum number (with ): is the quantum number of the orbit from which the electron passes into the lower orbit - i.e. from the third orbit to the second (see Bohr's atomic model ).
energy
The following applies to the energy of the emitted photon :
With
- Speed of light in a vacuum
- Planck's constant .
The same applies to the energy levels of the two above. Orbits in the atom (see Rydberg energy ):
- .
With it follows:
- .
After the meaning of the main quantum number in the term for the energy levels had been recognized, the terms term symbol and term scheme for related tools became established.
Spectral line series
With ( basic state ) and a series of spectral lines is obtained , which is also called the Lyman series . The first transition in the series has a wavelength of 121 nm, the series limit is 91 nm. The other series are similar:
Surname | Wavelength of the first transition (α line) |
converges towards the series limit |
||
---|---|---|---|---|
1 | 2 to ∞ | Lyman series | 121 nm | 91.13 nm |
2 | 3 to ∞ | Balmer series | 656 nm | 364.51 nm |
3 | 4 to ∞ | Paschen series | 1,874 nm | 820.14 nm |
4th | 5 to ∞ | Brackett series | 4,051 nm | 1458.03 nm |
5 | 6 to ∞ | Pound series | 7,456 nm | 2278.17 nm |
6th | 7 to ∞ | Humphreys series | 12,365 nm | 3280.56 nm |
Extensions
For hydrogen-like atoms
For hydrogen-like ions , i. H. Ions that only have a single electron, such as B. He + , Li 2+ , Be 3+ or Na 10+ , the above formula can be extended to:
With
- the atomic number , d. H. the number of protons in the atomic nucleus
- the effective principal quantum numbers corrected for the quantum defect .
For atoms with one valence electron
A further generalization on the light emission of atoms that have a single electron in their outermost shell , but below that possibly additional electrons in closed shells , leads to Moseley's law .
literature
- Joseph Reader, Charles H. Corliss: Line Spectra of the Elements . In: CRC Handbook of Chemistry and Physics
Web links
- Comprehensive database with 568 hydrogen emission lines from the National Institute of Standards and Technology (A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team (2014). NIST Atomic Spectra Database (ver. 5.2))