Lithium quantum numbers

The period (or row) of the periodic table m which an element appears corresponds to the principal quantum number of the highest numbered occupied orbital (n = 1 m the case of hydrogen and helium) Hydrogen and helium are first row elements lithium in = 2) IS a second row element... 

Which a — 2 orbital does the third electron in a lithium atom occupy Screening causes the orbitals with the same principal quantum number to decrease in stability as / increases. Consequently, the 2 S orbital, being more stable than the 2 orbital, fills first. Similarly, 3 S fills before 3 p, which fills before 3 d, and so on. 

The next element is lithium, with three electrons. But the third electron does not go in the Is orbit. The reason it does not arises from one the most important rules in quantum mechanics. It was devised by Wolfgang Pauli (and would result in a Nobel Prize for the Austrian physicist). The rule Pauli came up with is called the Pauli exclusion principle it is what makes quantum numbers so crucial to our understanding of atoms. 

The exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. The Is orbital has the following set of allowable numbers n= 1, f = 0, m = 0, mg = +1/2 or -1/2. All of these numbers can have only one value except for spin, which has two possible states. Thus, the exclusion principle restricts the Is orbital to two electrons with opposite spins. A third electron in the Is orbital would have to have a set of quantum numbers identical to those of one of the electrons already there. Thus, the third electron needed for lithium must go into the next higher energy shell, which is a 2s orbital. 

Each of a lithium atom s three electrons also has its own unique set of quantum numbers, as you can see helow. (Assume these quantum numbers represent a ground state lithium atom.)... 

Refer to the sets of quantum numbers for hydrogen and helium that you saw earlier. Then use the quantum numbers for lithium to infer why a lithium atom has the ground state electron configuration that it does. 

Turning now to lithium, we have two nuclides available for NMR measurements Li and Li. Both are quadrupolar nuclei with spin quantum number / of 1 and 3/2, respectively. The natural abundance of Li (92.6%) provides enough NMR sensitivity for direct measurements, but also Li (7.4%) can easily be observed without enrichment. However, isotopic enrichment poses no practical problem and is advantageous if sensitivity is important, as for measurements of spin-spin coupling constants in solution and of quadrupole coupling constants in the sohd state. 

Each orbital can therefore contain no more than two electrons, with opposite spin quantum numbers. This rule, which affects the order in which electrons may fill orbitals, is known as the Pauli exclusion principle. Table 2.3 summarizes the configuration of electron orbitals for the first three shells. The orbitals are labeled with the numerical value of n and a letter corresponding to the value of l (s, p, d, f..). As you can see from Table 2.3, the n = 1 shell can hold up to two electrons, both in the s orbital, the n - 2 shell can hold up to eight electrons (2 in the s and 6 in the p orbital), the n - 3 can hold up to 18 electrons (2 s, 6 p, and 10 d), and the n 4 shell can hold up to 32 electrons (2 s, 6 p, 10 d, and 14 f). The lowest energy orbitals are occupied first. So for hydrogen, which has one electron, the electron resides in the Is orbital. For lithium, which has three electrons, two are in the Is orbital and the third is in the 2s orbital. For silicon (Z = 14), there are two electrons in Is, two electrons in 2s, six electrons in 2p, two electrons in 3s, and two electrons in 3p. 

Note that all the superscripts for an atom must add up to the total number of electrons in the atom—1 for hydrogen, 3 for lithium, 11 for sodium, and so forth. Also note that the orbitals are not always listed in order of principal quantum number. The 4s orbital, for example, is lower in energy than the 3 dorbitals, as is indicated on the energy-level diagram of Figure 5-22. The 4s orbital, therefore, appears before the 3dorbitaI. 

All the atoms in a given period (a horizontal row of the periodic table) have a common valence shell, and the principal quantum number of that shell is equal to the period number. For example, the valence shell of elements in Period 2 (lithium to neon) is the shell with n = 2. All the atoms in one period have the same type of core. Thus the atoms of Period 2 elements all have a heliumlike Is2 core, denoted [He those of Period 3 elements have a neonlike s12s12p6 core, denoted [Ne]. 

With lithium (Z = 3) there are the two electrons in a spherical cloud (as with helium) plus a third electron. In most cases, in considering the electronic configurations of the element, the last electron is the only one that need be considered, all the remaining having been present in the preceding atom in the periodic table (there are a few important exceptions, however). For the third lithium electron there are no more possible combinations of quantum numbers where w = 1 since neither l or m can exceed zero if n is only one. The last (outermost) electron of lithium has the quantum numbers ... 

After the last electron goes into neon (Z — 10), there are no more possible combinations of quantum numbers having n = 2. The outermost electron of sodium must go into a higher energy state with n = 3, much farther from the nucleus. Thus, the outermost electron of sodium, like that of lithium, may be easily lost. More generally, since the chemical properties of elements are determined by their outermost (valence) electrons, the periodicity of properties naturally arises from the quantum restrictions. 

PROBLEM Assign quantum numbers to the valence electron of a lithium atom. 

A lithium atom has three electrons. The hrst two of these can have the same sets of quantum numbers as the two electrons of hehum. What should the set of quantum numbers for the third electron be We cannot choose the lowest permitted value for n, which is 1, because C and m would then both be 0. If we choose -j as the value of m, the third electron would have a set of quantum numbers exactly the same as that of one of the hrst two electrons, and if we choose the value = +5, the third electron would have the same set of quantum numbers as the other. Because neither of these situations is permitted by the Pauli principle, n cannot be 1 for the third electron. We must choose the next higher value, = 2. With = 2, the permitted values of are 0 and 1. Because = 0 wUl give a lower value for the sum + , we choose that value for . With = 0, must be 0, and we can choose either 5 or +5 for m. The quantum numbers for the three electrons of the Uthium atom can thus be as follows ... 

Let us consider the derivation of the electron configuration of the elements from lithium to neon which constitute the second period of Men el eff s classification. The distribution of the electrons in the ground positions of the atoms is given below. In the atom of lithium, the first two electrons occupy the u position, the third electron according to the Pauli principle must fall into the electron shell having the main quantum number equal to two. The electron accordingly occupies the position of minimum energy within this shell, which is the 2s orbital. 

The ionization energy tends to decrease down a group in the periodic table (for example, from lithium to sodium to potassium). As the principal quantum number increases, so does the distance of the outer electrons from the nucleus. There are some exceptions to this trend, however, especially for the heavier... 

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