Rydberg constant

The Rydberg constant is a named after Johannes Rydberg constant of nature in an approximate formula for the calculation of atomic spectra, see Rydberg formula. The value is expressed as a wavenumber ionization energy of the hydrogen atom, neglecting relativistic effects and the motion of the nucleus (ie, infinite nuclear mass, hence the index).

The amounts present ( CODATA 2010) recommended value of the Rydberg constant

The relative standard uncertainty of 5.0 × 10-12. This makes it the most accurately measured fundamental constant at all.

Context of other fundamental constants

Rydberg constant α is obtained and the Compton wavelength? C, e of an electron from the fine structure constant by

With

  • The mass of the electron
  • The speed of light
  • Planck's quantum of action
  • The elementary charge
  • The dielectric constant.

Rydberg frequency and Rydberg energy

The Rydberg constant is often expressed as a frequency or energy. The recommended values ​​be

  • Rydberg frequency:
  • Rydberg energy:

The specific value of the Rydberg energy is called a Rydberg so is the Rydberg used as unit of measurement for energy.

Derivation

The Rydberg constant can be calculated from the following four conditions:

  • The Bohr condition is

Where the radius of the electron orbit called.

  • For the centripetal force
  • Coulomb force between the electron and the singly charged atomic core
  • The electric potential energy of the electron is:

With the relationship of de Broglie we obtained from the Bohr condition:

For a stable web is considered classic

Substituting ( 1) gives the radius

Under the assumptions made, these are therefore the only permissible path radii.

Moreover, it follows from (2) for the kinetic energy of

And for the total energy

Substituting ( 3) gives

Each orbit thus has a certain potential and kinetic energy so that when a change in the orbit from n1 to n2 takes place a change in energy. This is just

Or

Written as a change in wavelength:

The Rydberg constant is therefore just

This result was first determined by Niels Bohr as a consequence of his model of the atom.

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