Azimuthal quantum number, defined

The orbital or azimuthal quantum number (/) defines form (i.e., eccentricity of elliptical orbit cf Pauling, 1948) and indicates which sub-level is occupied by the electron. It assumes integer values between 0 and n —. ... 

From equations (8), (9) and (10) it is evident that the path of the electron in the ith region is a segment of the KepleT ellipse defined by the segmentary radial and the azimuthal quantum numbers n and k, so that it can be described by the known equations... 

The principal and azimuthal quantum numbers are directly defined as n and l respectively. The 21+1 multiplicity of sub-levels defines the allowed values of the magnetic quantum number mi, on assuming the Bohr condition ... 

It turns out that there is not one specific solution to the Schrodinger equation but many. This is good news because the electron in a hydrogen atom can indeed have a number of different energies. It turns out that each wave function can be defined by three quantum numbers (there is also a fourth quantum number but this is not needed to define the wave function). We have already met the principal quantum number, n. The other two are called the orbital angular momentum quantum number (sometimes called the azimuthal quantum number), , and the magnetic quantum number, mi. 

We add a brief remark on the notation for the terms, A few lines above we have used capital letters S, P, D,. . , instead of small letters (p. 126). This is customary in the case of several electrons for the purpose of indicating the total orbital moment. It is also customary to define the multiplet character, that is to say, the number of terms belonging to a particular multiplet (all with the same principal and azimuthal quantum numbers), by attaching this number to the term symbol as a left-hand upper index also, the multiplicity written down is always the one which occurs when I is large, viz. 25+1. In fact,... 

Further, this derivation is altogether independent of whether an exchange of angular momentum between core and electron takes place or not, i.e. whether or not an azimuthal quantum number k can be defined in a manner analogous to that in the case of central motion. 

The second quantum number— the azimuthal quantum number, I—can have integral values from 0 to w — 1 for each value of n. This quantum number defines die shape of the orbital. (We will consider these shapes in Section 6.6.) The value of / for a particular orbital is generally designated by the letters s, p, d, and /, corresponding to / values of 0,1,2, and 3, respectively, as summarized here. 

The azimuthal quantum number t defines the subshells in a shell that are associated with the orbital angular... 

The atomic orbital wavefunctions come in sets that are associated with four different quantum numbers. The first is the principal quantum number, which takes on positive integer values starting with 1 (n = 1,2,3,...). Anatom s highest principal quantum number determines the valence shell of the atom, and it is typically only the electrons and orbitals of the valence shell that are involved in bonding. Each row in the periodic table indicates a different principal quantum number (with the exception of rf and f orbitals, which are displaced down one row from their respective principal shells). In addition, each row is further split into azimuthal quantum numbers (wi = 0,1,2,3,... alternatively described as s, p, d,f...). This number indicates the angular momentum of the orbital, and it defines the spatial distribution of the orbital with respect to the nucleus. These orbitals are shown in Figure 1.1 for = 2 (as with carbon) as a function of one of the three Cartesian coordinates. 

For the combination of terms we have the selection rule only even and odd terms combine. This forms the counterpart [Seitenstuck] to the Laporte rule in atoms, which can also be brought into this form if we define that terms are indicated as even or odd according to whether the sum of azimuthal quantum numbers of the electrons is even or odd, which represents their behaviour under reflection in the... 

There are an infinite number of solutions, each with a distinct energy (they are quantized). The solutions contain numbers that come in particular sets, which we defined as the principle, azimuthal, and magnetic quantum numbers in Chapter 1. Note that the solutions are nothing more than equations describing standing waves in three-dimensional space. The equations indicate an amplitude... 

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