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Rydberg Constant
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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 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):

:R_\infty = rac{m_e e^4}{(4 \pi \epsilon_0)^2 \hbar^3 4 \pi c} = 1.0973731568525(73) \cdot 10^7 \,\mathrm{m}^{-1}
:::where
:::: \hbar \ is the reduced Planck's Constant ,
:::: m_e \ is the Rest Mass of the Electron ,
:::: e \ is the Elementary Charge ,
:::: c \ is the Speed Of Light in Vacuum , and
:::: \epsilon_0 \ is the Permittivity Of Free Space .

This constant is often used in Atomic Physics in the form of an energy:
:h c R_\infty = 13.6056923(12) \,\mathrm{eV} \equiv 1 \,\mathrm{Ry}

The "infinity" constant appears in the formula:
:R_M = rac{R_\infty}{1+ rac{m_e}{M}}
:::where
::::R_M is the Rydberg constant for a certain Atom with one Electron with the Rest Mass m_e \
::::M \ is the mass of its Atomic Nucleus .


ALTERNATE EXPRESSIONS


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

:R_\infty = rac{\alpha^2 m_e c}{4 \pi \hbar} = rac{\alpha^2}{2 \lambda_e}
where
:: \alpha \ is the Fine-structure Constant , and
:: \lambda_e \ is the Compton Wavelength of the electron.


RYDBERG CONSTANT FOR HYDROGEN


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

R_H = 10967758 \pm 1 m^{-1}

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


SEE ALSO



REFERENCES

Mathworld