Rydberg constant

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The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ångström and Johann Balmer. Each chemical element has its own Rydberg constant, which can be derived from the "infinity" Rydberg constant.

The Rydberg constant is one of the most well-determined physical constants with a relative experimental uncertainty of less than 7 parts per trillion. The ability to measure the it directly to such a high precision confirms the proportions of the values of the other physical constants that define it.

The "infinity" Rydberg constant is (according to 2002 CODATA results):

<math>R_\infty = \frac{m_e e^4}{(4 \pi \epsilon_0)^2 \hbar^3 4 \pi c} = 1.0973731568525(73) \cdot 10^7 \,\mathrm{m}^{-1}</math>

where

<math> \hbar \ </math> is the reduced Planck's constant,

<math> m_e \ </math> is the rest mass of the electron,

<math>e \ </math> is the elementary charge,

<math> c \ </math> is the speed of light in vacuum, and

<math> \epsilon_0 \ </math> is the permittivity of free space.

This constant is often used in atomic physics in the form of an energy:

<math>h c R_\infty = 13.6056923(12) \,\mathrm{eV} \equiv 1 \,\mathrm{Ry}</math>

The "infinity" constant appears in the formula:

<math>R_M = \frac{R_\infty}{1+\frac{m_e}{M}}</math>

where

<math>R_M</math> is the Rydberg constant for a certain atom with one electron with the rest mass <math>m_e \ </math>

<math>M \ </math> is the mass of its atomic nucleus.

1 Alternate expressions
2 Rydberg Constant for hydrogen
3 See also
4 References

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Alternate expressions

The Rydberg constant can also be expressed as the following equations.

<math>R_\infty = \frac{\alpha^2 m_e c}{4 \pi \hbar} = \frac{\alpha^2}{2 \lambda_e} </math>

where

<math> \alpha \ </math> is the fine-structure constant, and

<math>\lambda_e \ </math> is the Compton wavelength of the electron.

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Rydberg Constant for hydrogen

Plugging in the rest mass of an electron and an atomic mass <math>M</math> of 1 for hydrogen, we find the Rydberg constant for hydrogen, <math> R_H </math>.

Plugging this constant into the Rydberg formula, we can obtain the emission spectrum of hydrogen.

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