Orbital magnetic quantum number

According to quantum mechanics, electrons in atoms occupy the allowed energy levels of atomic orbitals that are described by four quantum numbers the principal, the azimuthal, the magnetic, and the spin quantum numbers. The orbitals are usually expressed by the principal quantum numbers 1, 2, 3, —increasing from the lowest level, and the azimuthal quantum numbers conventionally eiqiressed by s (sharp), p (principal), d (diffuse), f (fundamental), — in order. For instance, the atom of oxygen with 8 electrons is described by (Is) (2s) (2p), where the superscript indicates the munber of electrons occupying the orbitals, as shown in Fig. 2-1. 

Principle quantum number n Orbital angular momentum quantum number / Magnetic quantum number nil Spin quantum number s Atomic orbital designation... 

The resulting RPAE equation for the photoionization amplitude Dn from an initial state i i into a final state V2, (v is the total set of quantum numbers that characterize a single-electron state the principal quantum number n, orbital quantum number /, magnetic quantum number mi, and the z projection of the electron spin sz) is given by [55]... 

Shell Principal quantum number n Angular momentum quantum number k Orbital designation Magnetic quantum number mjt Spin quantum number m Total number of electrons per orbital... 

The hydrogenic wave function in the position space for electron with principal quantum number n, orbital momentum quantum number /, and magnetic quantum... 

The periodic law is not of the physical but the chemical kind, although not often properly realized. It resides in the fact of attributing four quantum numbers (principal, orbital, magnetic, and spin) to each electron in arranging them in the so-called configuration by the aujbau principle according which the Periodic Table is constructed. Certainly, such quantum labeling... 

The coupling of S to the intemuclear axis is caused not by the electrostatic field, which has no effect on it, but by the magnetic field along the axis due to the orbital motion of the electrons. Figure 7.16(a) shows that the component of S along the intemuclear axis is Ffi. The quantum number F is analogous to Mg in an atom and can take the values... 

The third quantum number m is called the magnetic quantum number for it is only in an applied magnetic field that it is possible to define a direction within the atom with respect to which the orbital can be directed. In general, the magnetic quantum number can take up 2/ + 1 values (i.e. 0, 1,. .., /) thus an s electron (which is spherically symmetrical and has zero orbital angular momentum) can have only one orientation, but a p electron can have three (frequently chosen to be the jc, y, and z directions in Cartesian coordinates). Likewise there are five possibilities for d orbitals and seven for f orbitals. 

The third quantum number required to specify an orbital is mh the magnetic quantum number, which distinguishes the individual orbitals within a subshell. This quantum number can take the values... 

The spins of two electrons are said to be paired if one is T and the other 1 (Fig. 1.43). Paired spins are denoted Tl, and electrons with paired spins have spin magnetic quantum numbers of opposite sign. Because an atomic orbital is designated by three quantum numbers (n, /, and mt) and the two spin states are specified by a fourth quantum number, ms, another way of expressing the Pauli exclusion principle for atoms is... 

For each orbital listed in Exercise 1.51, give the possible values for the magnetic quantum number. 

Associated with the spin of an electron is a magnetic moment, which can be expressed by a quantum number of + or —5. According to the Pauli principle, any two electrons occupying the same orbital must have opposite spins, so the total magnetic moment is zero for any species in which all the electrons are paired. In... 

Among atomic orbitals, s orbitals are spherical and have no directionality. Other orbitals are nonspherical, so, in addition to having shape, every orbital points in some direction. Like energy and orbital shape, orbital direction is quantized. Unlike footballs, p, d, and f orbitals have restricted numbers of possible orientations. The magnetic quantum number (fflj) indexes these restrictions. 

The magnetic quantum number derives its name from the fact that different orbital orientations generate different behaviors in... 

As mentioned in Section Wl, an electron has magnetism associated with a property called spin. Magnetism is directional, so the spin of an electron is directional, too. Like orbital orientation, spin orientation is quantized Electron spin has only two possible orientations, up or down. The spin orientation quantum number )... 

Magnetic quantum number One solution to Schrodinger s wave equation produces the magnetic quantum number. It specifies how the s, p, d, and/orbitals are oriented in space. 

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