Energy sublevels

Electron energy sublevels in the order of increasing energy. The order shown is the order of sublevel filling as atomic number increases, starting at the bottom with 1 s. 

The periodic table and electron configurations. The periodic table can be used to deduce the electron configurations of atoms. The color code in the figure shows the energy sublevels being filled across each period. Elements marked with asterisks have electron configurations slightly different from those predicted by the table. 

The periodic table has an unusual shape because it is divided into blocks representing the energy sublevel being filled with valence electrons. In the periodic table shown in the diagram, which sequence lists these blocks in s-p-d-f order ... 

We have seen that a spin Hamiltonian in combination with its associated spin wavefunctions defines an energy matrix, which can always be diagonalized to obtain all the real energy sublevels of the spin manifold. Furthermore, the diagonaliza-tion also affords a new set of spin wavefunctions that are a basis for the diagonal matrix, and which are linear combinations of the initial set of spin functions. The coefficients in these linear combinations can be used to calculate the transition probabilities of all transitions within the spin manifold. 

In the periodic table on the next page, each energy sublevel, e.g. 2s, is placed in the elemental box which corresponds to the element, e.g. Be, in which that energy sublevel is filled. 

It was fairly straightforward to modify Bohr s model to include the idea of energy sublevels for the hydrogen spectrum and for atoms or ions with only one electron. There was a more fundamental problem, however. The model still could not explain the spectra produced by many-electron atoms. Therefore, a simple modification of Bohr s atomic model was not enough. The many-electron problem called for a new model to explain spectra of all types of atoms. However, this was not possible until another important property of matter was discovered. 

Regardless of its name, the second quantum number refers to the energy sublevels within each principal energy level. The name that this hook uses for the second quantum number is orbital-shape quantum number (i), to help you remember that the value of 1 determines orbital shape. (You will see examples of orbital shapes near the end of this section.)... 

To identify an energy sublevel (type of orbital), you combine the value of n with the letter of the orbital shape. For example, the sublevel with n = 3 and 7 = 0 is called the 3s sublevel. The sublevel with n = 2 and 7=1 is the 2p sublevel. 

The letters used to represent energy sublevels are abbreviations of names that nineteenth-century chemists used to describe the coloured lines in emission spectra. These names are sharp, principal, diffuse, and /undamental. 

In the lithium atom, and for all other multi-electron atoms, orbitals in different energy sublevels differ in energy. 

Boron s fifth electron must go into the 2p energy sublevel. Since 1=1, mi may be -1, 0, or +1. The fifth electron can go into any of these orbitals, because they all have the same energy. When you draw orbital diagrams, it is customary to place the electron in the first available box, from left to right. 

You may have noticed that period 3 ended with electrons filling the 3p energy sublevel. However, when n = 3,1 may equal 0, 1, and 2. Perhaps you wondered what happened to the 3d orbitals (7 = 2). 

Imagine that scientists have successfully synthesized element X, with atomic number 126. Predict the values of n and 1 for the outermost electron in an atom of this element. State the number of orbitals there would be in this energy sublevel. 

The rare earth (RE) ions most commonly used for applications as phosphors, lasers, and amplifiers are the so-called lanthanide ions. Lanthanide ions are formed by ionization of a nnmber of atoms located in periodic table after lanthanum from the cerium atom (atomic number 58), which has an onter electronic configuration 5s 5p 5d 4f 6s, to the ytterbium atom (atomic number 70), with an outer electronic configuration 5s 5p 4f " 6s. These atoms are nsnally incorporated in crystals as divalent or trivalent cations. In trivalent ions 5d, 6s, and some 4f electrons are removed and so (RE) + ions deal with transitions between electronic energy sublevels of the 4f" electroiuc configuration. Divalent lanthanide ions contain one more f electron (for instance, the Eu + ion has the same electronic configuration as the Gd + ion, the next element in the periodic table) but, at variance with trivalent ions, they tand use to show f d interconfigurational optical transitions. This aspect leads to quite different spectroscopic properties between divalent and trivalent ions, and so we will discuss them separately. 

The above considerations may also be formulated in a more general way, applying a most fruitful approach proposed by Fano in 1964 [142]. The essence of this approach consists of expanding over multipole moments either the matrix of collision relaxation rates Tmm, or the matrix of energy sublevel energies uimm — (Em — Em )/H, where Em is the energy shift of the M-sublevel energy due to perturbation. Thus, for instance, the multipole moment uJq of the u>mm> matrix is... 

The s, p, d, and f levels are also called energy sublevels. The s sublevel has one orbital, an 5 orbital. The p sublevel has three orbitals, x, y, and . The d sublevel has five orbitals and therefore a total capacity of ten electrons. Examine Figure 8.10 to see how the sublevel idea fits in with the concept of energy levels. 

Energy sublevels can be thought of as a section of seats in a theater. The rows that are higher up and farther from the stage contain more seats, just as energy levels that are farther from the nucleus contain more sublevels. 

Principal energy levels contain energy sublevels. Principal energy level 1 consists of a single sublevel, principal energy level 2 consists of two sublevels, principal energy level 3 consists of three sublevels, and so on. To better understand the relationship... 

Atomic orbitals represent the electron probability clouds of an atom s electrons. Q The spherical 1s and 2s orbitals are shown here. All s orbitals are spherical in shape and increase in size with increasing principal quantum number. The three dumbbell-shaped p orbitals are oriented along the three perpendicular X, y, and z axes. Each of the p orbitals related to an energy sublevel has equal energy. 

All orbitals related to an energy sublevel are of equal energy. For example, all three 2p orbitals are of equal energy. 

In a multi-electron atom, the energy sublevels within a principal energy level have different energies. For example, the three 2p orbitals are of higher energy than the 2s orbital. 

In order of increasing energy, the sequence of energy sublevels within a principal energy level is s, p, d, andf... 

Orbitals related to energy sublevels within one principal energy level can overlap orbitals related to energy sublevels within another principal level. For example, the orbital related to the atom s 4s sublevel has a lower energy than the five orbitals related to the 3d sublevel. 

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