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 Jun 19, 2025
-> The AAI ATC Exam 2025 will be conducted on July 14, 2025 for Junior Executive..
-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025.
-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.
-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.
-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).
-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.
-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).
-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.
-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.