Effective Nuclear Charge Definition

Table of Effective Nuclear Charges of the Atoms

Effective nuclear charge is the net charge an electron sees.
Effective nuclear charge is the net charge an electron sees. Science Photo Library - MEHAU KULYK, Getty Images

Effective Nuclear Charge Definition

The effective nuclear charge is the net charge an electron experiences in an atom with multiple electrons. The effective nuclear charge may be approximated by the equation:

Zeff = Z - S

Where Z is the atomic number and S is the number of shielding electrons

Higher energy electrons can have other lower energy electrons between the electron and the nucleus, effectively lowering the positive charge experienced by the high energy electron.

The shielding effect is the name given to the balance between the attraction between valence electrons and protons and the repulsion between valence and inner electrons. The shielding effect explains the trend in atomic size on the periodic table and also why valence electrons are readily removed from an atom.

Examples: A 2s lithium electron can have 2 1s electrons between itself and the lithium nucleus. Measurements indicate the effective nuclear charge experienced by a 2s lithium electron is 0.43 times the charge of the lithium nucleus.

Slater's rules may be used to calculate effective nuclear charge:

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
1s10.62611.609          12.59113.57514.55815.54116.52417.508
2s6.5717.392          8.2149.0209.82510.62911.43012.230
2p6.8027.826          8.9639.94510.96111.97712.99314.008
3s2.5073.308          4.1174.9035.6426.3677.0687.757
3p            4.0664.2854.8865.4826.1166.764
 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
2p15.02716.04117.05518.06519.07320.07521.08422.08923.09224.09525.09726.09827.09128.08229.07430.06531.05626.047
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
3d  7.1208.1418.9839.75710.52811.18011.85512.53013.20113.87815.09316.25117.37818.47719.55920.626
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
4d  15.95813.07211.23811.39212.88212.81313.44213.61814.76315.87716.94217.97018.97419.96020.93421.893
5p 8.4709.1029.99510.80911.61212.425

Reference

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.

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Helmenstine, Anne Marie, Ph.D. "Effective Nuclear Charge Definition." ThoughtCo, Apr. 11, 2018, thoughtco.com/definition-of-effective-nuclear-charge-605056. Helmenstine, Anne Marie, Ph.D. (2018, April 11). Effective Nuclear Charge Definition. Retrieved from https://www.thoughtco.com/definition-of-effective-nuclear-charge-605056 Helmenstine, Anne Marie, Ph.D. "Effective Nuclear Charge Definition." ThoughtCo. https://www.thoughtco.com/definition-of-effective-nuclear-charge-605056 (accessed May 24, 2018).