Magnetic Quantum Number mf

The magnetic quantum number, mf, determines the spatial orientation of the orbital s angular momentum and takes the values - to + . An s orbital ( - 0), being spherical, can only have one orientation in space—it does not point in any one direction and hence it only has one value for me(0). However, a p orbital could point in any direction. For a p orbital ( = 1) there are three values of file -1,0, and +1. These correspond to the p orbitals aligned along the mutually perpendicular x-, y-, and z-axes. These orbitals, designated p, py, and p, are all degenerate. They differ only in their spatial orientations. 

The principal quantum number is an integer (1, 2, 3,. ..) and represents the radial expansion of the orbital. The angular quantum number varies from 0 to (n — 1) and characterizes the shape of the orbital (designed by letters s,p, d,f, g,... for = 0,1, 2,3,4,...). The magnetic quantum number mf is the projection of the vector f onto the z axis and is linked to the orientation of the orbital in space it varies between and + . Finally, is the projection of the vector s and takes values of Vi. Pauli s principle requires that two electrons of the same atom must at least differ by the value of one quantum number, this implies that only two electrons of opposite spin can be associated with a given orbital. An electronic shell consists in all electrons having the same quantum number n. A sub-shell regroups electrons with same n and numbers, has therefore (2 + 1) orbitals, and may contain a maximum of (A + 2) electrons. The shapes of the seven 4f orbitals (n = 4, = 3) are represented on top of Fig. 1. 

The magnetic quantum number mf) describes the orientation of the orbital in space (to be discussed in Section 7.7). Within a subshell, the value of m depends on the value of the angular momentum quantum number, . For a certain value of , there are (2F + 1) integral values of m as follows ... 

For any value of the principal quantum number (n), the value 0 is possible for the angular momentum quantum number ( ), corresponding to an s subshell. Furthermore, when = 0, the magnetic quantum number (mf) has only one possible value, 0, corresponding to an s orbital. Therefore, there is an subsheU in every shell, and each i subsheU contains just one orbital, an s orbitaL... 

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