Effective nuclear charge – Wikipedia

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The Effective nuclear charge or simply effective charge (O Effective nuclear charge , in symbols

WITH eff{displaystyle Z_{mathrm {eff} }}

o Z*) is the charge of which an electron really suffers in a polyermony atom. It is said to be “effective” because, due to the screen effect of the other electrons of the most internal layers (in English core ), the electron at the last layer does not totally suffer from the nuclear charge.

Only in the hydrogen atom and in Elio’s atom, the electrons (respectively one for hydrogen and two for helium), not being shielded from more internal electrons, are affected by an effective charge equivalent to nuclear charge. In all other atoms, the electrons at the last layer are affected instead of an effective charge calculable by means of the equation:

where z* is the notally adopted notation to indicate the effective nuclear charge, Z is the number of protons and s is the average number of electrons ( screen constant ) between the nucleus and the electron considered and is easily calculable taking into account the rules of Slater.

A consequence of the actual charge is represented by the dimension of the atomic radius, which increases as the Z* decreases since the outermost electrons are less attracted by the Coulombian interaction with the nucleus and can therefore be more distant.

Effective nuclear charge (Z*) is a characteristic of each element of the periodic table of the elements. It increases slowly, along a group , from top to bottom [z*(li) = 1.3; Z*(na) = 2,22] or remains constant [z*(na) = 2,2; Z*(k) = 2,2] and along the period increases from left to right (screen effect partial ). The difference between the complete screen and partial screen effect deduces from the rules of Slater, which affirm that the shielding effect produced by the electrons belonging to the same shell of the electron is less considered that those placed in the lower shells. This, in fact, also affects the dimensions of the atomic radius: along the period decreases (the effective charge increases due to the partial shielding), while the atomic radius increases along the groups (the effective charge increases slowly due to the complete screen but the Atomic orbitals are more distant from the nucleus as the main quantum number increases).

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Updated values ​​of the screen constants were provided by Clementi et al . [first] [2]

2p 33.039 34.030 35.003 35.993 36,982 37,972 38.941 39,951 40,940 41,930 42,919 43,909 44,898 45.885 46,873 47,860 48,847 49.835
3s 21,843 22,664 23,552 24.362 25.172 25,982 26,792 27.601 28,439 29,221 30.031 30.841 31,631 32,420 33.209 33,998 34.787 35.576
3p 21.303 22.168 23.093 23,846 24,616 25,474 26.384 27.221 28.154 29.020 29,809 30,692 31.521 32,353 33.184 34.009 34.841 35,668
4s 12.388 13.444 14.264 14.902 15.283 16.096 17.198 17,656 18.582 18,986 19.865 20,869 21.761 22,658 23,544 24.408 25.297 26,173
3D 21,679 22,726 25,397 25,567 26.247 27.228 28,353 29,359 30.405 31.451 32,540 33.607 34.678 35,742 36,800 37,839 38.901 39,947
4p 10.881 11,932 12.746 13,460 14.084 14,977 15,811 16,435 17.140 17.723 18.562 19.411 20.369 21,265 22.181 23.122 24.030 24,957
5s 4.985 6.071 6.256 6.446 5.921 6.106 7.227 6.485 6.640 (empty) 6.756 8.192 9.512 10.629 11.617 12.538 13.404 14,218
4D 15,958 13.072 11.238 11.392 12.882 12.813 13.442 13,618 14,763 15.877 16,942 17,970 18,974 19,960 20,934 21,893
5p 8.470 9.102 9.995 10,809 11.612 12.425
  1. ^ E. Clementi, Raimondi, D. L., Atomic Screening Constants from SCF Functions , in J. Chem. Phys , vol. 38, n. 11, 1963, pp. 2686–2689, Bibcode: 1963jchph..38.2686C , DOI: 10.1063/1,1733573 .
  2. ^ E. Clementi, Raimondi, D. L.; Reinhardt, W. P., Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons , in Journal of Chemical Physics , vol. 47, 1967, pp. 1300–1307, Bibcode: 1967JChPh..47.1300C , DOI: 10.1063/1,1712084 .

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