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Origin and Categories of Magnetisms
Published in Chen Wu, Jiaying Jin, Frontiers in Magnetic Materials, 2023
The status of each electron is governed by four quantum numbers including the principal quantum number (n = 1, 2, 3, 4… represented by K, L, M, N…) to determine the energy level of the electron, the angular momentum quantum number (l = 0, 1, 2, 3… n–1 represented by s, p, d, f…) to determine the magnitude of the orbital angular momentum, the magnetic quantum number (ml= 0, ±1… ±l) to determine the orientation of the orbital angular momentum with respect to the magnetic field, and the magnetic spin quantum number (ms= ±1/2) for quantized spin angular momentum. For a many-electron atom, the arrangement of the electrons follows the Pauling exclusion principle, stating that no two electrons have exactly the same set of quantum numbers (Pauli, 1946). The electrons usually fill the shells from low to high energy levels, following the sequence of 1s, 2s, 2p, 3s, 3p… Due to the energy-level-interlaced problem, however, from the 4s subshell, the s subshells are preferentially filled prior to the d subshells. Such issue also applies to the filling of 5p and 6s subshells prior to the 4f subshell. The actual arrangement of the electrons can be described as 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6, which is well illustrated in the sequence following the dashed arrows in Figure 2.2.
O
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[general] Quantum number defining the orientation in space of an orbital for a given energy (n) and shape (ℓ); mℓ = −ℓ,…,0,…ℓ;. A sphere (ℓ = 1)or cloverleaf (ℓ = 1) can only be oriented in one way in space. On the other hand, orbitals that have different shapes, such as polar (ℓ=1) or cloverleaf (ℓ=2), can have an orientation in different directions. A third quantum number is therefore needed to define the orientation in space of the orbital. The magnetic quantum number is named this way since the different orientations of orbitals were first observed under the influence of an external magnetic field. This quantum number is one of three coordinates that result from solving the Schrödinger wave equations, providing the principal (n), angular (ℓ), and magnetic (mℓ) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom. In contrast to the Bohr model, which is a one-dimensional model that only uses one quantum number to describe the size with respect to the distribution of electrons in the atom. This quantum number subdivides the subshell into individual orbitals which hold the electrons; there are 2ℓ + 1 orbitals in each subshell. In this light, the s subshell has only one orbital, subsequently the p subshell has three orbitals, ensuing for the following electron shells.
Review of Solid State Physics
Published in Douglas S. McGregor, J. Kenneth Shultis, Radiation Detection, 2020
Douglas S. McGregor, J. Kenneth Shultis
In free space, a single atom has discrete quantized energy states for the orbital electrons. Further, the Pauli exclusion principle states that no two electrons of an atom can have the same values for the four quantum numbers (n, l, ml, ms), where n is the principle number, which determines the electron’s energy, l is the angular momentum quantum number, ml is the magnetic quantum number, and ms is the spin.
Study of thermomagnetic properties of the diatomic particle using hyperbolic function position dependent mass under the external hyperbolic magnetic and AB force
Published in Molecular Physics, 2022
Suci Faniandari, A. Suparmi, C. Cari
In this part, we discuss the behavior of the energy spectra with the natural units and the parameters used in our model are listed in Table 1. In Tables 2–4 we have presented the numerical results of the energy level of the three selected diatomic molecules, involving H2, LiH, and HCl. The energy level for the symmetrical modified Poschl-Teller potential under the influence of external hyperbolic magnetic and AB force for the H2 molecule is shown in Table 2. For each magnetic quantum number, the energy increases linearly with the increase of the quantum number. The presence of the external magnetic field has influenced the energy level to decrease to a small number. Meanwhile, the presence of the AB force only gives a small effect on the increases in the energy value of the system. These results are similar to the LiH and HCl diatomic molecules in Tables 3 and 4.