Rydberg Constant

The Rydberg Constant is a physical constant relating to the electromagnetic spectrum of an atom, it was named after the Swedish physicist Johannes Rydberg.

Rydberg Constant Explained

In 1885, Balmer a Swiss mathematician shown that the wavelength of the visible spectrum of the hydrogen atom can be expressed as

\(\large{\lambda = \frac{h m^2}{(m^2 – 4)}}\)

Janne Rydberg studied the spectra of different elements independently. Instead of using the wavelength λ, he began to use the wavenumber \(n\) (The number of waves per duration is known as the wavenumber).

Rydberg found then that many line series are well described with the expression:

\(\large{n = n_0 – \frac{N_0}{(m + m’)^2}}\)

where \(m\) is a natural number. The quantum defect \(m’\) and \(n_0\) are specific for a particular series.

\(N_0\) was found to be a universal constant. 

Later, Rydberg’s constant No was denoted by \(R_{\infty}\)

Rydberg Constant Equation

In 1913, Niels Bohr shown that R can be expressed as a combination of the speed of light in vacuum c, Planck’s constant h, the charge of electron e, and its mass m by

\(\large{R_{\infty} = \frac{m e^4}{8 \epsilon_0^2 h^3 c}}\)

\(\epsilon_0\) is the permittivity of vacuum.
\(m_e\) is mass of electron in rest 
\(\alpha\) is fine structure constant 
\(c\) is speed of light 
\(a_0\) is Bohr radius 
\(hbar\) is reduced planck constant 

Value of Rydberg Constant 

The value of this constant \(R_{\infty}\) 

In meters 10973731.568508(65) m-1


Does Rydberg constant have two values?

No, Rydberg’s constant is the value of the highest wavenumber that any photon can emit. i.e. 1.09 x 107 (m-1).
Another term is Rydberg’s energy constant, it corresponds to the energy of photons whose wavenumber is the Rydberg constant. i.e. 13.6 eV

Why do we use a deviation spectrometer for determining the Rydberg constant?

We use spectrometers to analyze the interaction of matter and electromagnetic radiation by recording the wavelengths of photons emitted by different chemical sources.
In calculating this constant, we use a standard ‘prism spectrometer’.

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