Energy effective nuclear charge

Which of the following concepts underlies all the others ionization energy, effective nuclear charge, atomic size ... 

Table 5.2 Oitoital energies, effective nuclear charges, and screening constants for n=3 orbitals In sodnim...

Strategy Consider effective nuclear chaige and electron configuration to compare the ionization energies. Effective nuclear charge increases from left to right in a period (thus increasing IE), and it is more difficult to remove a paired core electron than an unpaired valence electron. 

The decrease in atomic radius moving across the periodic table can be explained in a similar manner. Consider, for example, the third period, where electrons are being added to the third principal energy level. The added electrons should be relatively poor shields for each other because they are all at about the same distance from the nucleus. Only the ten core electrons in inner, filled levels (n = 1, n = 2) are expected to shield the outer electrons from the nucleus. This means that the charge felt by an outer electron, called the effective nuclear charge, should increase steadily with atomic number as we move across the period. As effective nuclear charge increases, the outermost electrons are pulled in more tightly, and atomic radius decreases. 

As well as being attracted to the nucleus, each electron in a many-electron atom is repelled by the other electrons present. As a result, it is less tightly bound to the nucleus than it would be if those other electrons were absent. We say that each electron is shielded from the full attraction of the nucleus by the other electrons in the atom. The shielding effectively reduces the pull of the nucleus on an electron. The effective nuclear charge, Z lle, experienced by the electron is always less than the actual nuclear charge, Ze, because the electron-electron repulsions work against the pull of the nucleus. A very approximate form of the energy of an electron in a many-electron atom is a version of Eq. 14b in which the true atomic number is replaced by the effective atomic number ... 

Account for the fact that the ionization energy of potassium is less than that of sodium despite the latter having the smaller effective nuclear charge. 

All the elements in a main group have in common a characteristic valence electron configuration. The electron configuration controls the valence of the element (the number of bonds that it can form) and affects its chemical and physical properties. Five atomic properties are principally responsible for the characteristic properties of each element atomic radius, ionization energy, electron affinity, electronegativity, and polarizability. All five properties are related to trends in the effective nuclear charge experienced by the valence electrons and their distance from the nucleus. 

As the value of n increases, d- and /-electrons become less effective at shielding the outermost, highest-energy elec-tron(s) from the attractive charge of the nucleus. This higher effective nuclear charge makes it more difficult to oxidize the metal atom or ion. 

To calculate the energy functions W and W2 it is necessary to evaluate the three integrals Haa, Hab and Sab. It is noted that the variational constant k has the same role as an effective nuclear charge in hydrogenic functions. The normalized functions ls and lsB are therefore of the form... 

Based upon Slater s rules, we have found that the effective nuclear charge increases sharply between periods one and three and then stays at 2.20 for the rest of the alkali metal group. You may recall that the ionization energy for an element can be calculated by using the equation ... 

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