Question

What is Rydberg’s constant? What is its value?

Answer 1

Hint: We calculate the wavelength of the spectral lines during electronic transition in an atom using the Rydberg’s formula. This formula uses Rydberg's constant in it.

Complete step by step answer:
-To calculate wavelengths of spectral lines in any chemical element we use the Rydberg’s formula.
In 1888 a Swedish physicist named Johannes Rydberg was the first one to give this formula and named the constant used in it to be Rydberg’s constant.
This formula gives a direct generalization of the equations used while calculating the wavelengths of hydrogen spectral series.

-For hydrogen this formula can be written as:
 $\dfrac{1}{{{\lambda _{vac}}}} = {R_H}\left( {\dfrac{1}{{{n_1}^2}} - \dfrac{1}{{{n_2}^2}}} \right)$
   Where, ${\lambda _{vac}}$ = wavelength of electromagnetic radiation emitted in vacuum;
                ${R_H}$ = Rydberg constant for hydrogen = $1.097 \times {10^7}{m^{ - 1}}$ ,
                 ${n_1}$ = principal quantum number of an energy level,
                 ${n_2}$ = principal quantum number of an energy level for the atomic electron transition
Here: ${n_2} > {n_1}$ .

-For any hydrogen like element this formula can be written as:
    $\dfrac{1}{\lambda } = R{Z^2}\left( {\dfrac{1}{{{n_1}^2}} - \dfrac{1}{{{n_2}^2}}} \right)$
   Where, λ = wavelength of light emitted in vacuum;
                R = Rydberg constant,
               ${n_1}$ = principal quantum number of the upper energy level,
               ${n_2}$ = principal quantum number of the lower energy level for the atomic electron transition

-The Rydberg’s constant is a physical constant which relates to the electromagnetic spectrum of an atom. The Rydberg formula for the hydrogen spectral series needed an empirical fitting parameter, from where the Rydberg’s constant arrived. But later on it was Neil Bohr who proved that more fundamental constants via the Bohr’s model could also help us calculate its value.
-The limiting value of the highest wave number of any photon that can be emitted from an atom or wavenumber of the lowest energy photon which is capable of ionizing an atom from its ground state can be expressed using this constant.
-The value of the Rydberg’s constant is = $1.09678 \times {10^7}{m^{ - 1}}$ $ \approx 1.97 \times {10^7}{m^{ - 1}}$

Note: All this calculation done above of the wavelength using Rydberg’s formula and Rydberg’s constant is done on the basis of Bohr’s atomic model. This model explains the atomic spectrum of hydrogen, other atoms and also ions. The emission spectrum of hydrogen is then divided into spectral lines (whose wavelength we calculate using this formula) which are formed due to electronic transitions. Also these spectral lines can lie in Lyman, Balmer, Paschen or Bracket series.