Rydberg formula

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The Rydberg formula in a manuscript by Johannes Rydberg

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

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:

Energy levels of the hydrogen spectrum
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

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

Web links