Quantum numbers letter designation

The introduction of an external magnetic field provides the most convenient reference axis for trii. The values of nil are determined by the / quantum number. For each value of I there are (21 + 1) values of m/. For historical reasons the 0,1, 2, and 3 values of the / quantum number are designated by the letters s, p, d, and f, respectively. (This choice is a relic of early spectroscopic studies when certain spectral series were designated sharp, principal, diffuse, or fundamental. )... 

Sub-levels within the same principle quantum number are designated by an integer value appearing as a subscript following the capital letter. The value of 1 is used for the level containing electrons most tightly bound to the nuclei, and subsequent sub-levels are denoted in ascending order. Thus, the 2s level is represented as Lj and the 2p y2 and 2pj/2 levels are referred to as the L2 and L3 levels, respectively. 

Another method is commonly used to designate sublevels. Instead of giving the quantum number , the letters s, p, d, or f indicate the sublevels = 0,1, 2, or 3, respectively. That is,... 

The second quantum number is called the angular momentum quantum number. It is designated by the letter f and can be thought of as representing a subshell within a principal energy... 

The angular momentum quantum numbers are often given letter designations, so that when they are stated along with principal quantum numbers, less confusion results. The letter designations of importance in the ground states of atoms are the following ... 

The orbital angular-momentum quantum number, , defines the shape of the atomic orbital (for example, s-orbitals have a spherical boundary surface, while p-orbitals are represented by a two-lobed shaped boundary surface). can have integral values from 0 to (n - 1) for each value of n. The value of for a particular orbital is designated by the letters s, p, d and f, corresponding to values of 0, 1, 2 and 3 respectively (Table 1.2). 

However, in most cases Ls is only a small perturbation on the energy. The wave functions are primarily constructed from functions which are eigenfunctions of L and S, so that we can characterize a given state by giving its L and 5 quantum numbers. The value of L is designated by a letter symbol ... 

In the development of the concepts of atomic structure much of the experimental evidence came from optical and x-ray spectroscopy, From this work certain notations have arisen that are now an accepted part of the language. For example, the n = I shell is sometimes known as the K-shell, the n 2 shell as the L-shell. the it = 3 shell as the JM-shell. etc., with consecutively following letters of the alphabet being used to designate those shells with successively higher principal quantum numbers. A Roman numeral subscript further subdivides the shells in accordance with the n, J, and j quantum numbers of the electrons, as shown in Table 4,... 

A letter notation has been given to the different orbital angular momentum states by optical spectroscopists. In this notation an I = 0 state is called an s state (not to be confused with the v used as u quantum number for spin, and which can usually he distinguished from die way it is used), an I = I stale is a p stale an I = 2 a d state, an 1 = 3 state an f stale, with consecutively higher letters above / in the alphabet designating each succeeding value of / A number often accompanies the state designation to indicate the appropriate value of n. For example, a ip level is un n = 3. I = I stale. 

The designations of the other coupling schemes are more cumbersome and less obvious. They can be easily obtained from formulas (11.3)—(11.5). For LK and jK coupling the levels may be denoted as XKJ or X[K]j, where X = L,j. Quantum number L may be designated both using letters or numbers. For example, for the npn p configuration there are the... 

An energy state for an electron in an atom is denoted by writing the numerical value of the principal quantum number followed by a letter to denote the l value. The letters used to designate the / values 0, 1, 2, 3,. .. arc, v, p, d, f,. .., respectively. These letters have their... 

Because only n and values affect the energies of electrons, the electrons with the same n value and the same value all have the same energy. In other words, all the electrons in a given subshell are degenerate. Each subshell is denoted by its principal quantum number and the letter designation for . For example, for neon, with atomic number 10, the sets of quantum numbers for the 10 electrons are listed in Table 4.2. We can group them as follows ... 

Table 3.2 Letter designations of angular momentum quantum numbers...

As mentioned in section 1.1.6 Wave functions and orbitals the angular momentum quantum number / determines the shape of the orbital while the magnetic quantum number mi determines the orientation of the orbital relative to the nucleus. Each orbital is designated with a letter dependent of the value of the angular momentum quantum number / ... 

In the following example we are going to look at the designation of letters and quantum numbers for different orbitals. 

Orbital. Each allowed combination of n, I, and mi values specifies one of the atom s orbitals. Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation. You can easily give the quantum numbers of the orbitals in any sublevel if you know the sublevel letter designation and the quantum number hierarchy. For example, the 2s sublevel has only one orbital, and its quantum numbers are n = 2, I = 0, and mi = 0. The 3p sublevel has three orbitals one with n = 3, / = 1, and nii = -1 another with n = 3, I = 1, and / / = 0 and a third with n = 3, I = 1, and m/ = -t-1. 

Symbols for the states of atoms are analogous to the symbols for the orbitals of single electrons. Thus the capital letters S, P, D, F, G, H. .. are used to designate states with L = 0, 1, 2, 3, 4, 5. .. The use of S for both a state and a quantum number is unfortunate, but in practice seldom causes any difficulty. The complete symbol for a state also indicates the total spin, but not directly in terms of the value of 5. Rather, the number of different Ms values, which is called the spin multiplicity, is used. Thus, for a state with 5 = 1, the spin multiplicity is 3 because there are three Ms values, 1,0, — 1. In general the spin multiplicity is equal to 25+1, and is indicated as a left superscript to the symbol for L. The following examples should make the... 

Table 7.1 The Angular Momentum Quantum Numbers and Corresponding Letters Used to Designate Atomic Orbitals...

The first four levels of orbitals in the hydrogen atom are listed with their quantum numbers in Table 7.2. Note that each set of orbitals with a given value of (sometimes called a subshell) is designated by giving the value of n and the letter for . Thus an orbital where n = 2 and = 1 is symbolized as 2p. There are three 2p orbitals, which have different orientations in space. We will describe these orbitals in the next section. 

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