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Instead, the Rydberg constant is inferred from measurements of atomic transition frequencies in three different atoms (hydrogen, deuterium, and antiprotonic helium). Detailed theoretical calculations in the framework of quantum electrodynamics are used to account for the effects of finite nuclear mass, fine structure, hyperfine splitting, and ...
For a hydrogen atom, the role of reduced mass is most simply seen in the Bohr model of the atom, where the reduced mass appears in a simple calculation of the Rydberg constant and Rydberg equation, but the reduced mass also appears in the Schrödinger equation, and the Dirac equation for calculating atomic energy levels.
Rydberg constant: 10 973 731.568 157 ... and is strongly dependent on how those units are defined. For example, the atomic mass constant is exactly known ...
The Rydberg constant is known to seven parts in a trillion. The mass of the electron relative to that of caesium and rubidium atoms is also known with extremely high precision. If the mass of the electron can be measured with sufficiently high precision, then α can be found from the Rydberg constant according to
It is traditionally divided to a normal mass shift (NMS) resulting from the change in the reduced electronic mass, and a specific mass shift (SMS), which is present in multi-electron atoms and ions. The NMS is a purely kinematical effect, studied theoretically by Hughes and Eckart. [ 3 ]
The exact value of the Rydberg constant assumes that the nucleus is infinitely massive with respect to the electron. For hydrogen-1, hydrogen-2 ( deuterium ), and hydrogen-3 ( tritium ) which have finite mass, the constant must be slightly modified to use the reduced mass of the system, rather than simply the mass of the electron.
It is now apparent why Rydberg atoms have such peculiar properties: the radius of the orbit scales as n 2 (the n = 137 state of hydrogen has an atomic radius ~1 μm) and the geometric cross-section as n 4. Thus, Rydberg atoms are extremely large, with loosely bound valence electrons, easily perturbed or ionized by collisions or external fields.
(typically between 1 eV and 10 3 eV), where R ∞ is the Rydberg constant, Z is the atomic number, n is the principal quantum number, h is the Planck constant, and c is the speed of light. For hydrogen-like atoms (ions) only, the Rydberg levels depend only on the principal quantum number n.