Chemical Sciences: A Manual for CSIRUGC National Eligibility Test for Lectureship and JRF/Rydberg constant
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The Rydberg constant, named after physicist Johannes Rydberg, is a physical constant that apperas in the Rydberg formula. It was 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 welldetermined 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.
For a series of discrete spectral lines emitted by atmoic hydrogen,
 .
The "infinity" Rydberg constant is (according to 2002 CODATA results):

 where
 is the reduced Planck's constant,
 is the rest mass of the electron,
 is the elementary charge,
 is the speed of light in vacuum, and
 is the permittivity of free space.
 where
This constant is often used in atomic physics in the form of an energy:
The "infinity" constant appears in the formula:

 where
 is the Rydberg constant for a certain atom with one electron with the rest mass
 is the mass of its atomic nucleus.
 where
Alternate expressions[edit  edit source]
The Rydberg constant can also be expressed as the following equations.
and
where
 is Planck's constant,
 is the speed of light in a vacuum,
 is the finestructure constant,
 is the Compton wavelength of the electron,
 is the Compton frequency of the electron,
 is the reduced Planck's constant, and
 is the Compton angular frequency of the electron.
Rydberg Constant for hydrogen[edit  edit source]
Plugging in the rest mass of an electron and an atomic mass of 1 for hydrogen, we find the Rydberg constant for hydrogen, .
Plugging this constant into the Rydberg formula, we can obtain the emission spectrum of hydrogen.
Derivation of Rydberg Constant[edit  edit source]
The Rydberg Constant can be derived using Bohr's condition, centripetal acceleration, and Potential Energy of the electron to the nucleus.
Bohr's condition,
where
 is some integer
 is the radius of some atom
Centripetal Acceleration,
where
PE of Attraction between Electron and Nucleus
where
 is the elementary charge,
 is the permittivity of free space.
Firstly we substitute into Bohr's condition, then solve for We obtain
We equate centripetal acceleration and attraction between nucleus to obtain
Substitute in and solve for we obtain
We know that
Substitute into this energy equation and we get
Therefore a chance in energy would be
We simply change the units to wave number () and we get where
 is Planck's constant,
 is the rest mass of the electron,
 is the elementary charge,
 is the speed of light in vacuum, and
 is the permittivity of free space.
 and being the excited states of the atom
We have therefore find the Rydberg constant for Hydrogen to be