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** Azimuthal quantum number, defined **

** Quantum number, azimuthal electron-spin **

** Quantum number, azimuthal magnetic **

** Quantum number, azimuthal orbital angular momentum **

** Quantum number, azimuthal radial **

** Quantum number, azimuthal rotational **

s orbitals are states with 1 = 0 and zero orbital angular momentum. The p orbitals with / = 1 have orbital angular momenta of V2 units of hiIn, while the d orbitals with 1 = 2 have V6 h 2n units of orbital angular momenta. [Pg.9]

The bound states (where < 0) are characterized by the three quantum numbers n (the principal quantum number), I (the azimuthal quantum number) and mi (the magnetic quantum number). [Pg.155]

It has been found possible to evaluate s0 theoretically by means of the following treatment (1) Each electron shell within the atom is idealised as a uniform surface charge of electricity of amount — zte on a sphere whose radius is equal to the average value of the electron-nucleus distance of the electrons in the shell. (2) The motion of the electron under consideration is then determined by the use of the old quantum theory, the azimuthal quantum number being chosen so as to produce the closest approximation to the quantum... [Pg.678]

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... [Pg.687]

According to the old quantum theory, the orbit of an electron moving in such a field consists of a number of elliptical segments. Each segment can be characterized by a segmentary quantum number n, in addition to the azimuthal quantum number Ic, which is the same for all segments. In all cases it is found that about half of the entire orbit lies in the outermost (j.th) region. [Pg.713]

The shell theory has had great success in accounting for many nuclear properties (3). The principal quantum number n for nucleons is usually taken to be n, + 1, where nr, the radial quantum number, is the number of nodes in the radial wave function. (For electrons n is taken to be nr + / +1 / is the azimuthal quantum number.) Strong spin-orbit coupling is assumed,... [Pg.816]

In addition to size, an atomic orbital also has a specific shape. The solutions for the Schrodinger equation and experimental evidence show that orbitals have a variety of shapes. A second quantum number indexes the shapes of atomic orbitals. This quantum number is the azimuthal quantum number (1). [Pg.470]

The azimuthal quantum number (1) can be zero or any positive integer smaller than n ... [Pg.471]

The wave functions nlm) for the hydrogen-like atom are often called atomic orbitals. It is customary to indicate the values 0, 1, 2, 3, 4, 5, 6, 7,. .. of the azimuthal quantum number / by the letters s, p, d, f, g, h, i, k,. .., respectively. Thus, the ground-state wave function 100) is called the Is atomic orbital, 200) is called the 2s orbital, 210), 211), and 21 —1) are called 2p orbitals, and so forth. The first four letters, standing for sharp, principal, diffuse, and... [Pg.176]

Although the expectation value r )ni cannot be obtained from equation (6.70), it can be evaluated by regarding the azimuthal quantum number I as the parameter in the Hellmann-Feynman theorem (equation (3.71)). Thus, we have... [Pg.186]

It will be identified in Chapter 6 as the azimuthal quantum number, which is characteristic of the two-body problem. [Pg.270]

The three quantum numbers may be said to control the size (n), shape (/), and orientation (m) of the orbital tfw Most important for orbital visualization are the angular shapes labeled by the azimuthal quantum number / s-type (spherical, / = 0), p-type ( dumbbell, / = 1), d-type ( cloverleaf, / = 2), and so forth. The shapes and orientations of basic s-type, p-type, and d-type hydrogenic orbitals are conventionally visualized as shown in Figs. 1.1 and 1.2. Figure 1.1 depicts a surface of each orbital, corresponding to a chosen electron density near the outer fringes of the orbital. However, a wave-like object intrinsically lacks any definite boundary, and surface plots obviously cannot depict the interesting variations of orbital amplitude under the surface. Such variations are better represented by radial or contour... [Pg.10]

quantum numbers had been proposed, based on spectral lines and inferences about electron energy levels a principal quantum number to specify energy level of the atom an azimuthal quantum number to specify the angular momentum of electrons moving elliptically and an inner or magnetic quantum number to express the orientation of the plane of the electron s orbit in a magnetic field. 20... [Pg.248]

The second quantum number describes an orbital s shape, and is a positive integer that ranges in value from 0 to (n - 1). Chemists use a variety of names for the second quantum number. For example, you may see it referred to as the angular momentum quantum number, the azimuthal quantum number, the secondary quantum number, or the orbital-shape quantum number. [Pg.134]

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. [Pg.15]

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 —. ... [Pg.13]

The wavefunction of an electron associated with an atomic nucleus. The orbital is typically depicted as a three-dimensional electron density cloud. If an electron s azimuthal quantum number (/) is zero, then the atomic orbital is called an s orbital and the electron density graph is spherically symmetric. If I is one, there are three spatially distinct orbitals, all referred to as p orbitals, having a dumb-bell shape with a node in the center where the probability of finding the electron is extremely small. (Note For relativistic considerations, the probability of an electron residing at the node cannot be zero.) Electrons having a quantum number I equal to two are associated with d orbitals. [Pg.71]

Electronic parameters include the number of electrons, the number of valence electrons in the outer orbit, the orbital quantum numbers n, the azimuthal quantum number or spdf status, electron radius and energy, polarizability, dipole moment, quadrupole moment, and first ionization energy. [Pg.157]

The filling of atomic orbitals follows an n + , n) orbital scheme known as the Madelung [75-77] or Klechkovskii [78] rule. In this orbital scheme, the electron occupies free states with the smallest value of the sum A = + of the principal quantum number n and the azimuthal quantum number ( according to the Pauli exclusion principle. In the presence of several states with identical N, the state with... [Pg.15]

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** Azimuthal quantum number, defined **

** Quantum number, azimuthal electron-spin **

** Quantum number, azimuthal magnetic **

** Quantum number, azimuthal orbital angular momentum **

** Quantum number, azimuthal radial **

** Quantum number, azimuthal rotational **

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