Question
Download Solution PDFIn the Rydberg formula for the spectrum of the hydrogen atom, the wavenumber is _____.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The Rydberg formula is the mathematical formula to determine the wavelength of light emitted by an electron moving between the energy levels of an atom. When an electron shift from an orbital from higher energy to lower energy state, a photon of light is generated. Rydberg formula is given by
- \(\bar\nu=\frac{1}{\lambda}=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})\)
where \(\bar\nu\) is wave number,
\(\lambda\) is wavelength,
\(R_H=\text{ Rydberg constant }=109677cm^{-1}=1.09\times10^{7}m^{-1}\)
Explanation:
- \(\bar\nu=\frac{1}{\lambda}=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})\)
- \(R_H=\frac{me^4}{8h^3c\epsilon_0^2}=1.09677\times10^{7}m^{-1}\)
- \(\bar\nu=\frac{1}{\lambda}=\frac{me^4}{8h^3c\epsilon_0^2}(\frac{1}{n_1^2}-\frac{1}{n_2^2})cm^{-1}\)
\(\implies\bar\nu\propto e^4\)
Hence, the correct answer is Option-2-directly proportional to the fourth power of an electron charge.
Last updated on May 26, 2025
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