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Home / Physics / Rydberg Constant

Rydberg Constant: Learn its Definition, Value, Units, Formula, Derivation and Applications

Last Updated on Feb 21, 2025
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Rydberg constant is a fundamental constant used in atomic physics. It is used in the calculations of wavelengths or frequencies of light. It was developed by a Swedish physicist named Johannes Rydberg while experimenting with a series of hydrogen spectra.

Read on to learn more about its formula, steps to calculate, and applications.

What is Rydberg Constant?

The Rydberg constant establishes the mathematical relationship between one spectral line to the next of an element. When an electron changes from one orbit to another or from a lower energy level to a higher energy state, it produces a photon of light, which is absorbed by that atom. Rydberg’s constant says that there is an integer relationship between wavelengths of successive lines in atomic spectra. The value of this constant is based on the fact that the atom which is emitting light is larger than the orbiting electron.

Rydberg constant symbol is denoted by

or

Rydberg Constant Value

Rydberg Constant Value,R∞

10973731.568508(65) m-1

Rydberg Constant Value,R∞

1.097 x 107m-1

Units of Rydberg Constant and Their Values​

The following table displays the different values for

Unit Value
Meters
Electron volt 13.605 eV
Joules
Angstrom

Rydberg Constant Dimensional Formula

The dimensional formula for the Rydberg constant is .

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Rydberg Constant Formula

The fundamental formula for Rydberg’s constant is 

It is a wavenumber association with the electromagnetic spectrum of each element. Along with the successive Bohr’s model, Rydberg came up with an equation. The Rydberg Constant for hydrogen is

Where, Z is the atomic number and and are the integers of the electromagnetic spectrum. Depending on the number of and , we understand which family of series an atom belongs to. For example, the Balmer series, Paschen series, Brackett series or Lyman series.

Rydberg Constant Derivation

The following context is the derivation of energies using the Rydberg constant for a Hydrogen atom.

Consider an electron contained in an orbit which is balanced by centripetal force and coulomb’s force,

Total energy E = kinetic energy (KE) + potential energy (PE)

The electric potential energy

Total energy (E) ,

+e is the charge of a proton and -e is the charge of an electron

- equation (1)

The centripetal force is equal to the the electrostatic force,

And

And

– equation (2)

Substituting equation (2) in equation (1)

- equation (3)

Is the equation for the total energy equation of an electron.

Since we are working with Bohr’s radius, quantized angular momentum shall be given by,

L = mvr

mvr = nh,

Where n = energy level of an atomic spectrum and h = planck’s constant.

-equation (4)

Substituting equation (3) in equation (2),

This equation is known as the Bohr radius for a hydrogen atom. – equation (5)

Substituting equation (5) in equation (3)

Hence the energy level of an nth orbit,

is the mass of an electron.

The difference between the energy levels for an electron from its initial energy and final energy in an atomic spectra,

where ,

is the value of Rydberg’s constant.

The equation for wavelength becomes,

Rydberg Constant Value

The fundamental formula for Rydberg’s constant is

Its value is,

Application of Rydberg Constant

Following are the applications of Rydberg Constant.

  1. Calculates the wavelength of the hydrogen spectrum.
  2. Used in calculating the ionization energies of the transmitted electron.
  3. Their potential and kinetic energies

Hope this article was informative and helpful for your studies and exam preparations. Stay tuned to the Testbook app for more updates and topics related to Physics and various such subjects. Also, reach out to the test series available to examine your knowledge regarding related exams.

If you are checking Rydberg Constant, also check the related physics articles:
Fine Structure Constant Stefan Boltzman Constant
Gravitational Constant Boltzmann Constant

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Rydberg Constant FAQs

The value of the Rydberg constant is

It is a function of atomic physics, used in hydrogen spectra to calculate wavenumber.

Rydberg constant is different for different elements,For example,For hydrogen = For deuterium = For lithium =

The Rydberg constant is not a universal constant.

is the value of Rydberg constant in joules.

The value of Rydberg constant for hydrogen in angstrom is .
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