Subshell number

Energy Level, n Type of Subshell Number of Subshells... 

SHELL (ENERGY LEVEL) SUBSHELL NUMBER OF ORBITALS ELECTRON CAPACITY... 

Principal Shell (n) Number of Subshells in the Principal Shell Identity of Subshells Number of Orbitals in the Subshell... 

Energy Level Shell Subshell Number of Electrons Energy Level Shell Subshell Number of Electrons... 

The subshell number, /, defines the orbital shape. Its values start at (n - 1), and become smaller by integer values, ending at zero. 

Ans. Three new quantum numbers appear, which characterize atomic structure in finer detail. These are /, the subshell number, a quantum number which specifies orbital shape, m, which specifies the orbitals orientation in space, and s, the spin quantum number, which describes the fact that electrons appear to rotate or spin on their axes. 

Ans. The values which the orbital quantum number can take depend upon the values of the subshell number I, as in the following chart. The orbital quantum number does not directly depend upon the principal quantum number n. 

Principal quantum number (n) Angular momentum quaiitum number (/) Magnetic quantum number (m) Subshells Number of orbitals Maximum number of electrons... 

Subshell Number of orbitals Total number of possible electrons in each orbital... 

When chemists describe one particular subshell in an atom, they can use both the n value and the subshell letter — 2p, 3d, and so on. Normally, a subshell value of 4 is the largest needed to describe a particular subshell. If chemists ever need a larger value, they can create subshell numbers and letters. 

In 1934 W. M. Elsasser, then working in France, discussed evidence showing that there is a special stability associated with certain numbers of protons and certain numbers of neutrons. These numbers, which are known as magic numbers, are 2, 8, 20, 28, 50, 82, and 126. The numbers can be correlated with the subshell numbers that have been developed in the discussion of the electrons in atoms. The magic number 2 is, of... 

For atoms having an atomic number greater than 10, the electron filling the inner shell vacancy may come from one of several possible subshells, each at a different energy, resulting in families of characteristic X-ray energies, e.g., the Ka, P family, the La, P, y family, etc. 

Consider now the solutions of the spherical potential well with a barrier at the center. Figure 14 shows how the energies of the subshells vary as a function of the ratio between the radius of the C o barrier Rc and the outer radius of the metal layer R ui- The subshells are labeled with n and /, where n is the principal quantum number used in nuclear physics denoting the number of extrema in the radial wave function, and / is the angular momentum quantum number. 

There is no single best form of the periodic table since the choice depends on the purpose for which the table is used. Some forms emphasize chemical relations and valence, whereas others stress the electronic configuration of the elements or the dependence of the periods on the shells and subshells of the atomic structure. The most convenient form for our purpose is the so-called long form with separate panels for the lanthanide and actinide elements (see inside front cover). There has been a lively debate during the past decade as to the best numbering system to be used for the individual... 

This problem clearly did not worry Stoner, who just went ahead and assumed that three quantum numbers could be specified in many-electron atoms. In any case, Stoner s scheme solved certain problems present in Bohr s configurations. For example, Bohr had assigned phosphorus the configuration 2,4,4,41, but this failed to explain the fact that phosphorus shows valencies of three and five. Stoner s configuration for phosphorus was 2,2,2,4,2,2,1, which easily explains the valencies, since it becomes plausible that either the two or the three outermost subshells of electrons form bonds. 

Our earlier discussion of off-diagonal s, however, indicated that 2Q would substantially exceed in many-electron systems. Consequently, if Eq. 34 is used with N an empirical factor,31 we may expect the N values to exceed substantially the actual number of electrons of the outer subshell. 

Slater-Kirkwood theory N = no. of electrons of outer subshell empirical evaluated from EL and correlate with actual number of electrons of both outer subshell and of whole system. 

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... 

There are 2/ + 1 different values of trij for a given value of / and therefore 2/ + 1 orbitals in a subshell of quantum number /. For example, when / = 1, mj= +1,0, — 1 so there are three p-orbitals in a given shell. Alternatively, we can say that a subshell with / = 1 consists of three orbitals. 

The hierarchy of shells, subshells, and orbitals is summarized in Fig. 1.30 and Table 1.3. Each possible combination of the three quantum numbers specifies an individual orbital. For example, an electron in the ground state of a hydrogen atom has the specification n = 1, / = 0, nij = 0. Because 1=0, the ground-state wavefunction is an example of an s-orbital and is denoted Is. Each... 

FIGURE 1.30 A summary of the arrangement of shells, subshells, and orbitals in an atom and the corresponding quantum numbers. Note that the quantum number m, is an alternative label for the individual orbitals in chemistry, it is more common to use x, y, and z instead, as shown in Figs. 1.36 through 1.38. 

There are three /7-orbitals in each subshell, corresponding to the quantum numbers / = +1, 0, —1. However, chemists commonly refer to the orbitals according to the axes along which the lobes lie hence, we refer to px, / v, and />. orbitals (Fig. 1.36). 

The location of an electron in an atom is described by a wavefunction known as an atomic orbital atomic orbitals are designated by the quantum numbers , l, and mi and fall into shells and subshells as summarized in Fig. 1.30. 

Write the subshell notation (3d, for instance) and the number of orbitals having the following quantum numbers ... 

In the d block, the energies of the (n — l )d-orbitals lie below those of the ns-orbitals. Therefore, the ws-electrons are lost first, followed by a variable number of (n — 1 )d-electrons. For example, to obtain the configuration of the Fe3+ ion, we start from the configuration of the Fe atom, which is [Ar]3d 64s2, and remove three electrons from it. The first two electrons removed are 4s-electrons. The third electron comes from the Id-subshell, giving [Ar 3d5. 

Those subshells that occur (are occupied) with only the value 1 for the quantum number n contribute only to the outer layer of spherons (the mantle). 

The Structural Basis of the Magic Numbers.—Elsasser10 in 1933 pointed out that certain numbers of neutrons or protons in an atomic nucleus confer increased stability on it. These numbers, called magic numbers, played an important part in the development of the shell model 4 s it was found possible to associate them with configurations involving a spin-orbit subsubshell, but not with any reasonable combination of shells and subshells alone. The shell-model level sequence in its usual form,11 however, leads to many numbers at which subsubshells are completed, and provides no explanation of the selection of a few of them (6 of 25 in the range 0-170) as magic numbers. 

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... 

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