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Basic Physics of X-ray Interactions in Matter
Published in Paolo Russo, Handbook of X-ray Imaging, 2017
This energetic change is associated with the absorption (j < i) or emission (j > i) of electromagnetic radiation. In 1888, Rydberg devised a similar Rydberg formula, which was used to predict the wavelengths of photons emitted by changes in the energy level of an electron in a hydrogen atom (Ritz 1908). In order to calculate the energy of the emission lines, and inspired by Rydberg, Moseley (1913) found empirically that E(Kα)=h⋅(3.29⋅1015)⋅3⋅(Z−1)24E(Lα)=h⋅(3.29⋅1015)⋅5⋅(Z−7.4)236
Introduction to Quantum Mechanics
Published in Caroline Desgranges, Jerome Delhommelle, A Mole of Chemistry, 2020
Caroline Desgranges, Jerome Delhommelle
Another proof of the validity of this theory comes from the Rydberg formula, which can be used to calculate the spectral emission lines of atomic hydrogen. Indeed, using Bohr’s atomic model, several different series of emission lines can be defined. According to Bohr, an atom is composed of electrons and of a nucleus. Electrons revolve around the nucleus on specific orbits. The distance between the nucleus and an electron on a specific orbit can be found using the following formula: nλ = 2πr. For example, for the closest orbit n = 1, the distance between the nucleus and the electron is 0.0529 nm, also known as the Bohr radius. Bohr proposes to calculate the energies of these specific orbits for the hydrogen atom and other hydrogen-like atoms and ions. Indeed, electrons can only gain and lose energy by jumping from one orbit to another, absorbing or emitting an electromagnetic radiation of frequency ν determined by the Planck relation: ΔE = E2 – E1 = hν. Nowadays, we use the Rydberg formula for hydrogen-like atoms, which is a generalization of the previous formula: 1/λ = RH(1/n12 – 1/n22) with n1 the principal quantum number for the upper energy level and n2 the corresponding quantum number for the lower energy level of the atomic electron transition. For n1 = 1 and n2 = 2 → ∞, the series is called the Lyman series (see Figure 3.12). For n1 = 2 and n2 = 3 → ∞, it is called the Balmer series. n1 = 3 and n2 = 4 → ∞ gives the Paschen series. Bohr receives the Nobel Prize 1922 “for his services in the investigation of the structure of atoms and of the radiation emanating from them”.
Ultralong-range Rydberg molecules
Published in Molecular Physics, 2020
Christian Fey, Frederic Hummel, Peter Schmelcher
The basic properties of diatomic ULRMs are illustrated in Figure 1(a–d). As shown in Figure 1(a), ULRMs consist of a ground-state atom and a Rydberg atom. The latter possesses an ionic core and an excited valence electron that interacts with the ground-state atom, which is sometimes also called ‘perturber’. Exemplary Born–Oppenheimer PECs for the case of a Rb ULRM close to the n = 30 Rydberg state are presented in Figure 1(b). At large internuclear separations, where interactions between the atoms are negligible, here for R>1900 Bohr radii , the PEC are nearly flat and correspond to energy levels of the isolated Rydberg atom with principal quantum number n and angular momentum l. These energies can be expressed by the Rydberg formula with an l-dependent quantum defect that describes deviations from the hydrogen spectrum due to core penetration. In this context one distinguishes low-l states with substantial quantum defects from high-l hydrogen-like states, which are shielded from the ionic core by a sufficiently large centrifugal barrier and have almost vanishing quantum defects. For instance the Rydberg spectrum of Rb is well approximated [49] by , , , and , which leads to the ordering of energy levels depicted in Figure 1(b).