Effective nuclear charge

The effective nuclear charge (often symbolized as or ) is the net positive charge experienced by an electron in a polyelectronic atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons. The effective nuclear charge experienced by the electron is also called the core charge. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom. Most of the physical and chemical properties of the elements can be explained on the basis of electronic configuration. Consider the behavior of ionization energies in the periodic table. It is known that the magnitude of ionization potential depends upon the following factors:

(a) Size of atom

(b)The nuclear charge

(c)The screening effect of the inner shells

(d)The extent to which the outermost electron penetrates into the charge cloud set up by the inner lying electron.


Calculations

In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated from Coulomb's law.

However, in an atom with many electrons, the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:

where

Z is the number of protons in the nucleus (atomic number), and
S is the shielding constant.

S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater). Douglas Hartree defined the effective Z of a Hartree–Fock orbital to be:

where

is the mean radius of the orbital for hydrogen, and
is the mean radius of the orbital for a proton configuration with nuclear charge Z.

Values

Updated effective nuclear charge values were provided by Clementi et al. in 1963 and 1967.[1][2] In their work, screening constants were optimized to produce effective nuclear charge values that agree with SCF calculations. Though useful as a predictive model, the resulting screening constants contain little chemical insight as a qualitative model of atomic structure.

Effective Nuclear Charges
  H   He
Z1   2
1s1.000   1.688
  LiBe   BCNOFNe
Z34   5678910
1s2.6913.685   4.6805.6736.6657.6588.6509.642
2s1.2791.912   2.5763.2173.8474.4925.1285.758
2p     2.4213.1363.8344.4535.1005.758
  NaMg   AlSiPSClAr
Z1112   131415161718
1s10.62611.60912.59113.57514.55815.54116.52417.508
2s6.5717.3928.2149.0209.82510.62911.43012.230
2p6.8027.8268.9639.94510.96111.97712.99314.008
3s2.5073.3084.1174.9035.6426.3677.0687.757
3p4.0664.2854.8865.4826.1166.764
  KCaScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr
Z192021222324252627282930313233343536
1s18.49019.47320.45721.44122.42623.41424.39625.38126.36727.35328.33929.32530.30931.29432.27833.26234.24735.232
2s13.00613.77614.57415.37716.18116.98417.79418.59919.40520.21321.02021.82822.59923.36524.12724.88825.64326.398
2p15.02716.04117.05518.06519.07320.07521.08422.08923.09224.09525.09726.09827.09128.08229.07430.06531.05632.047
3s8.6809.60210.34011.03311.70912.36813.01813.67614.32214.96115.59416.21916.99617.79018.59619.40320.21921.033
3p7.7268.6589.40610.10410.78511.46612.10912.77813.43514.08514.73115.36916.20417.01417.85018.70519.57120.434
4s3.4954.3984.6324.8174.9815.1335.2835.4345.5765.7115.8425.9657.0678.0448.9449.75810.55311.316
3d7.1208.1418.9839.75710.52811.18011.85512.53013.20113.87815.09316.25117.37818.47719.55920.626
4p 6.2226.7807.4498.2879.0289.338
  RbSrYZrNbMoTcRuRhPdAgCdInSnSbTeIXe
Z373839404142434445464748495051525354
1s36.20837.19138.17639.15940.14241.12642.10943.09244.07645.05946.04247.02648.01048.99249.97450.95751.93952.922
2s27.15727.90228.62229.37430.12530.87731.62832.38033.15533.88334.63435.38636.12436.85937.59538.33139.06739.803
2p33.03934.03035.00335.99336.98237.97238.94139.95140.94041.93042.91943.90944.89845.88546.87347.86048.84749.835
3s21.84322.66423.55224.36225.17225.98226.79227.60128.43929.22130.03130.84131.63132.42033.20933.99834.78735.576
3p21.30322.16823.09323.84624.61625.47426.38427.22128.15429.02029.80930.69231.52132.35333.18434.00934.84135.668
4s12.38813.44414.26414.90215.28316.09617.19817.65618.58218.98619.86520.86921.76122.65823.54424.40825.29726.173
3d21.67922.72625.39725.56726.24727.22828.35329.35930.40531.45132.54033.60734.67835.74236.80037.83938.90139.947
4p10.88111.93212.74613.46014.08414.97715.81116.43517.14017.72318.56219.41120.36921.26522.18123.12224.03024.957
5s4.9856.0716.2566.4465.9216.1067.2276.4856.640(empty)6.7568.1929.51210.62911.61712.53813.40414.218
4d15.95813.07211.23811.39212.88212.81313.44213.61814.76315.87716.94217.97018.97419.96020.93421.893
5p 8.4709.1029.99510.80911.61212.425

See also

References

  1. Clementi, E.; Raimondi, D. L. (1963). "Atomic Screening Constants from SCF Functions". J. Chem. Phys. 38 (11): 2686–2689. Bibcode:1963JChPh..38.2686C. doi:10.1063/1.1733573.
  2. Clementi, E.; Raimondi, D. L.; Reinhardt, W. P. (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". Journal of Chemical Physics. 47: 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.

Resources

  • Brown, Theodore; LeMay, H.E.; & Bursten, Bruce (2002). Chemistry: The Central Science (8th revised edition). Upper Saddle River, New Jersey 07458: Prentice-Hall. ISBN 0-13-061142-5.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.