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Quantum Mechanics and Its Applications
Published in Sergey Edward Lyshevski, Nano- and Micro-Electromechanical Systems, 2018
where RR is the Rydberg constant, RR = 1.097373 × 107m−1. Example 7.1Let the electron jump from n1 = 3 to n2 = 2 and from n1 = 6 to n2 = 5. One can calculate the corresponding wavelengths. We have λ=11.097373×107(322232−22)=656nm;λ=11.097373×107(625262−52)=7455.8nm
Introduction
Published in George K. Knopf, Kenji Uchino, Light Driven Micromachines, 2018
In Equation (1.3), n1 and n2 are both integers and kR is the proportionality constant known as the Rydberg constant. The Rydberg constant represents the limiting value of the wavenumber, or wave frequency, of the lowest-energy photon capable of ionizing the hydrogen atom from its ground state.
Atomic Spectral Series, ca. 1860-1920
Published in John C.D. Brand, Lines of Light, 2017
was the asymptotic limit of (4) as a approached zero. Thereafter Rydberg used the Balmer law to fix the constant Rfor all elements. He felt that (4) gave random residuals attributable to (supposedly) random errors of wavelength measurement, though given the vagaries of published wavelengths the judgment called for a generous measure of faith. The constant R was later named the Rydberg constant in recognition of this work. Originally, Rydberg used R = 109721.6 cm−1, derived from air wavelengths on the old Ångstrom scale, and we must do the same if we are to reproduce his calculations.
High-precision Ramsey-comb spectroscopy on molecular deuterium for tests of molecular quantum theory
Published in Molecular Physics, 2023
Charlaine Roth, Andrés Martínez de Velasco, Elmer L. Gründeman, Mathieu Collombon, Maximilian Beyer, Vincent Barbé, Kjeld S. E. Eikema
Comparing experimentally measured transition frequencies in atoms and molecules with those obtained from theory calculations is a powerful method to test our understanding of the fundamental laws of physics. However, calculations of the energy levels does require accurate values of the fundamental constants. By measuring different transitions within one system, and by measuring in different systems, it is possible to disentangle the laws of physics from the constants and determine both. For many decades, atomic hydrogen has been a cornerstone for such spectroscopic tests [1,2], and it enables a very accurate determination of the Rydberg constant and the proton charge radius. Surprisingly, spectroscopic measurements in muonic hydrogen (with a bound muon instead of an electron) led to a substantially different proton radius and Rydberg constant [3,4]. New measurements in normal (electronic) hydrogen now tend to confirm the smaller proton radius from the muonic results [5,6], but not all of them [7,8]. Moreover, a significant 7σ discrepancy still exists for the deuteron charge radius (although no new measurements have been published) [9]. This history has made clear that measurements need to be done in different systems. Molecules are very interesting in that respect because they have extra degrees of freedom (vibration and rotation) that enable tests of a different nature and of different fundamental constants. An example is the recent determination of the proton to electron mass ratio from spectroscopy of HD ions [10,11].