Matematiska och systemtekniska institutionen

Janne Rydberg


Fysik och Skolteknik

The Rydberg constant

In 1885, the Swiss mathematician Balmer showed that the wavelength of the visible spectrum of the hydrogen atom can be described by the formula

λ = hm2/(m2 − 4),

Independently, Janne Rydberg analyzed the spectra of many elements. He started using the wavenumber n instead of the wavelength lambda. The wavenumber is the number of waves per length. Rydberg found then that many line series are well described with the expression:

n = no − No/(m+m')2,

where m is a natural number. The quantum defect m' and no and are specific for a particular series. No turns out to be a universal constant, the Rydberg constant. Rydberg showed that the Balmer series of hydrogen is a special case with m'=0, no=4No.

Now Rydberg's constant No is denoted by R. In 1913, Niels Bohr showed that R can be expressed as a combination of the speed of light in vacuum c, Planck's constant h, the electrons charge e, and its mass m by

R=me4/(8εo2h3c),
where εo is the permittivity of vacuum.

Value

The 1998 accepted value of the Rydberg constant R∞ is:
  • 10 973 731.568 548(83) m-1
  • 3.289 841 960 367(25).1015 Hz (Rc)
  • 13.605 691 72(53) eV (Rhc/e)
  • 2.179 871 90(17).10-18 J (Rhc)

Matematiska och systemtekniska institutionen
Vejdes plats 6 och 7, Växjö universitet, 351 95 Växjö.
Telefon: 0470-70 80 00. Fax: 0470-840 84.
Ansvarig: Pieter Kuiper