Principal electronic shell

For the periodic table it is important that all orbitals with the same value of n are in the same principal electronic shell and all orbitals with the same n and I are in the same subshell. The number of orbitals in a subsheU is the same as the number of allowed values of m. Instead of using numerical values for I it is customary to use letter symbols, as the spectroscopists did long before the introduction of the quantum mechanics (see Table 3.7). 

All orbitals with the same value of n are in the same principal electronic shell or principal level, and all orbitals with the same n and values are in the same subshell, or sublevel. 

Principal electronic shells are numbered according to the value of n. The first principal shell consists of orbitals with n = 1 the second principal shell of orbitals with n = 2 and so on. The value of n relates to the energy and most probable distance of an electron from the nucleus. The higher the value of n, the greater the electron energy and the farther, on average, the electron is from the nucleus. The principal quantum number, therefore, has a physical signifi-... 

The number of subshells in a principal electronic shell is the same as the number of allowed values of the orbital angular momentum quantum number, . In the first principal shell, with n = 1, the only allowed value of is 0, and there is a single subshell. The second principal shell n = 2), with the allowed values of 0 and 1, consists of two subshells the third principal shell n = 3) has three subshells (f = 0,1, and 2) and so on. Or, to put the matter in another way, because there are n possible values of the quantum number, that is, 0,1,2,... (n - 1), the number of subshells in a principal shell is equal to the principal quantum number. As a result, there is one subshell in the principal shell with n = 1, two subshells in the principal shell with n = 2, and so on. The name given to a subshell, regardless of the principal shell in which it is found, depends on the value of the i quantum number. The first four subshells are... 

Based on the relationship between electron configurations and the periodic table, give the number of (a) outer-shell electrons in an atom of Sb ft)) electrons in the fourth principal electronic shell of Pt (c) elements whose atoms have six outer-shell electrons (d) unpaired electrons in an atom of Te (e) transition elements in the sixth period. 

The first set of screening constants was obtained from the discussion of the motion of an electron in the field of the nucleus and its surrounding electron shells, idealized as electrical charges uniformly distributed over spherical surfaces of suitably chosen radii. This idealization of electron shells was first used by Schrodinger3), and later by Heisenberg4) and Unsold5), who pointed out that it is justified to a considerable extent by the quantum mechanics. The radius of a shell of electrons with principal quantum number nt is taken as... 

A distinguishing feature of electronically excited atoms and molecules is that they have one or a few excited orbitals of an electron. The principal properties of these particles are represented by a high internal energy potential localized on the excited orbitals and the structure of electron shell essentially different from the electron ground state. 

Although following similar nuclear reaction schemes, nuclear analytical methods (NAMs) comprise bulk analysing capability (neutron and photon activation analysis, NAA and PAA, respectively), as well as detection power in near-surface regions of solids (ion-beam analysis, IB A). NAMs aiming at the determination of elements are based on the interaction of nuclear particles with atomic nuclei. They are nuclide specific in most cases. As the electronic shell of the atom does not participate in the principal physical process, the chemical bonding status of the element is of no relevance. The general scheme of a nuclear interaction is ... 

All electrons in atoms can be described by means of these four quantum numbers and, as first enunciated in 1926 by Pauli in his Exclusion Principle, each electron in an atom must have a unique set of the four quantum numbers. A summary of the electron shells and of the corresponding maximum numbers of orbitals, and electrons, is shown in Table 4.2 where each shell is defined by the value of the principal quantum number (K = 1, L = 2, etc. according to X-ray spectroscopy nomenclature). 

The possible states of electrons are called orbitals. These are indicated by what is known as the principal quantum number and by a letter—s, p, or d. The orbitals are filled one by one as the number of electrons increases. Each orbital can hold a maximum of two electrons, which must have oppositely directed spins. Fig. A shows the distribution of the electrons among the orbitals for each of the elements. For example, the six electrons of carbon (B1) occupy the Is orbital, the 2s orbital, and two 2p orbitals. A filled Is orbital has the same electron configuration as the noble gas helium (He). This region of the electron shell of carbon is therefore abbreviated as He in Fig. A. Below this, the numbers of electrons in each of the other filled orbitals (2s and 2p in the case of carbon) are shown on the right margin. For example, the electron shell of chlorine (B2) consists of that of neon (Ne) and seven additional electrons in 3s and 3p orbitals. In iron (B3), a transition metal of the first series, electrons occupy the 4s orbital even though the 3d orbitals are still partly empty. Many reactions of the transition metals involve empty d orbitals—e.g., redox reactions or the formation of complexes with bases. 

The orbitals are completely described by specifying three quantum numbers, but only two are used in this hook. The principal quantum number (symbolized n) is a whole number, 1 or greater, that identifies the electron shell of the orbital, where the lower digits denote shells of lower energy that are closer to the atomic nucleus. The second quantum number (symbolized 1) is a whole number from 0 up to n — 1 that defines the type of orbital within a shell (n). For historical reasons, the different shapes of orbitals are represented by letters. (See Table 4-1.)... 

A familiar way of handling this question is offered by the notion of electronic shells. By definition, an electronic shell collects all the electrons with the same principal quantum number. The K shell, for example, consists of U electrons, the L shell collects the 2s and 2p electrons, and so on. The valence shell thus consists of the last occupied electronic shell, while the core consists of all the inner shells. This segregation into electronic shells is justified by the well-known order of the successive ionization potentials of the atoms. 

Figure 1.1 Principal features of the periodic table. The International Union of Pure and Applied Chemistry (IUPAC) now recommends Arabic group numbers 1-18 in place of the traditional Roman I—VIII (A and B). Group names include alkali metals (1), alkaline earth metals (2), coinage metals (11), chalcogens (16), and halogens (17). The main groups are often called the s,p block, the transition metals the d, block elements, and the lanthanides and actinides the / block elements, reflecting the electronic shell being filled. (See inside front cover for detailed structure of the periodic table.)...

Physically natural states of the system correspond to invariant subspaces of P(L2(]r3) 0 (02) electronic shell with principal quantum number... 

The atomic radii of the second- and third-series transition elements from group 4B on are nearly identical, though we would expect an increase in size on adding an entire principal quantum shell of electrons. The small sizes of the third-series atoms are associated with what is called the lanthanide contraction, the general decrease in atomic radii of the /-block lanthanide elements between the second and third transition series (Figure 20.4). 

Principal quantum number A number (n = 1, 2, 3,. ..) that describes the location of an electron shell (energy level) around the nucleus of an atom (compare with orbital, shell, and subshell). 

Subshell One or more orbitals in an electron shell of an atom. Subshells are designated s, p, d, and f. The s, p, d, and f subshells contain a maximum of 2, 6, 10, and 14 electrons, respectively (compare with orbital and principal quantum number). 

Atomic orbitals are grouped into different shells at different distances from the nucleus. Each shell is identified by a principal quantum number n, with n = 1 for the lowest-energy shell closest to the nucleus. As n increases, the shells are farther from the nucleus, higher in energy, and can hold more electrons. Most of the common elements in organic compounds are found in the first two rows of the periodic table, indicating that their electrons are found in the first two electron shells. The first shell (n = 1) can hold two electrons, and the second shell (n = 2) can hold eight. 

The radial wave function R(r) depends on two quantum numbers, n and /. The principal quantum number, n, determines the electron shell. The numbers n = 1, 2, 3, 4,. .. correspond to the shells K, L, M, N, respectively. For the hydrogen atom, n completely deter-... 

In general, for a particular value of the principal quantum number, there cannot be more than two s, six />, ten d and fourteen/ electrons and the total possible number of electrons for a given value of n is therefore equal to 2n. Thus the introduction of the concept of spin leads to the doubling of the number of possible electronic states (equation 1.39). The possible distribution of electrons for a hydrogen like atom is shown in Table V and it is seen that the series 2, 8, 18, 32,. . . which has arisen from the application of the Pauli principle is in agreement with the numbers of elements occurring in the periodic table of Mendeleeff. The electron shells with values for the principal quantum number i, 2, 3, 4, etc are often referred to as the /if, L, Af, JV, etc shells. 

The pairing of electrons is important, because it confers a degree of stability on the species concerned. Electrons in an atom are contained within atomic orbitals, each of which may only hold a maximum of two electrons. The electron in a hydrogen atom is contained in the first principal quantum shell, which is indicated by 1. Within this principal quantum shell, there is only one type of subshell, and this is represented by the letter s . The electronic configuration of hydrogen may be written as Is1. The raised postscript indicates that there is only one electron in that particular orbital. 

The two electrons in helium are both contained within the first principal quantum shell. Write down the electronic configuration of helium. 

In the second principal quantum shell, there are four subshells, one s and three p subshells, each of which may contain two electrons, which gives a total of eight electrons in all at the second level. 

The electron that was added to the helium atom to form the anion could not fit into the s subshell of the first principal quantum shell, because it already had two electrons and so was full. Instead, this extra electron occupied the next available orbital, which was the s subshell of the second principal quantum level. This requires a lot of energy, and so it is difficult. Hence, the He- anion, which it should also be noted is a radical species, is not normally found. 

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