Question

Rydberg constant is:
A. Same for all elements
B. Different for different elements
C. A universal constant
D. Is different for lighter elements but same for heavier elements

Answer 1

Hint:Generally the constant has fixed value. Rydberg constant is given by Johannes Rydberg. He gave the formula to calculate the wavelength for Balmer series. According to that the value of Rydberg constant depends upon the atomic number.

Formula used:
\[{{\text{R}}_{\text{H}}}{\text{=}}\,\dfrac{{{{\text{m}}_{\text{e}}}{{\text{e}}^{\text{4}}}}}{{{8\varepsilon }_{\text{o}}^{\text{2}}{{\text{h}}^{\text{3}}}{\text{c}}}}\]

Complete step-by-step answer:In the hydrogen spectrum, the transition from higher energy level to energy level of principle quantum number two produces the line that lies invisible. These lines are known as the Balmer series.
Johannes Rydberg gave the formula for the Balmer series of the hydrogen spectrum. The formula to determine the wavelength of transitions in hydrogen emission spectrum is as follows:
\[\dfrac{{\text{1}}}{\lambda } = \,{{\text{R}}_{\text{H}}}{{\text{Z}}^2}\left[ {\dfrac{{\text{1}}}{{{\text{n}}_{{\text{Lower}}}^{\text{2}}}} - \dfrac{{\text{1}}}{{{\text{n}}_{{\text{higher}}}^2}}} \right]\]
Where,
\[\lambda \] is the wavelength.
Z is the atomic number.
\[{{\text{R}}_{\text{H}}}\] is the Rydberg constant.
The value of Rydberg constant is as follows:
\[{{\text{R}}_{\text{H}}}\, = \,\dfrac{{{{\text{m}}_{\text{e}}}{{\text{e}}^{\text{4}}}}}{{8\varepsilon _{\text{o}}^{\text{2}}{{\text{h}}^{\text{3}}}{\text{c}}}}\]
Where,
\[{{\text{m}}_{\text{e}}}\] is the mass of electron
\[{\text{e}}\] is the change of electron
\[\varepsilon_{\text{o}}\] is the permittivity of vacuum
\[{\text{h}}\] is the Planck's constant
\[{\text{c}}\] is the speed of light

\[\dfrac{{\text{1}}}{\lambda }
=\dfrac{{{{\text{m}}_{\text{e}}}{{\text{e}}^{\text{4}}}}}{{8\varepsilon_{\text{o}}^{\text{2}}{{\text{h}}^{\text{3}}}{\text{c}}}}{{\text{Z}}^2}\left[ {\dfrac{{\text{1}}}{{{\text{n}}_{{\text{Lower}}}^{\text{2}}}} - \dfrac{{\text{1}}}{{{\text{n}}_{{\text{higher}}}^2}}} \right]\]
According to the wavelength formula of the hydrogen emission spectrum the value of Rydberg constant is directly proportional to the atomic number.
${{\text{R}}_{\text{H}}}\, \propto {{\text{Z}}^{\text{2}}}$
Every element of the periodic table has a different atomic number, so the Rydberg constant value is different for every element.
For hydrogen atom the value of Rydberg constant in per centimetre is $109678\,{\text{c}}{{\text{m}}^{ - 1}}$
So, Rydberg constant is different for different elements.

Therefore, option (B) Different for different elements is correct.

Note:Atomic number is the number of protons. Universal means the constant should have one value. Rydberg constant is not universal. Its value changes according to the atomic number. The Planck constant, Boltzmann constant or gas constant are the universal constant because these have fixed values.