Definition of effective nuclear charge is quite obvious. But, for example, If I take Fe atom and average out all the effective nuclear charge for 1s to 3d , it will give me another number. What will this number signifies ?
Reference : http://en.wikipedia.org/wiki/Effective_nuclear_charge
As far as I know, the average nuclear charges need advanced Hartree-Fock solutions. Especially the Ionization Conjecture of the HF theory. The issue is a difficult theme in computational physics. Several related publications could be accessed through Google Scholar and Scopus
We teachers will make our graduate level students to calculate Z* of all the elements of the periodic table by Slater’s rule. The following are the simple points which one needs to apply:
1) Write the electron configuration for the atom using the following design;
(1s)(2s,2p)(3s,3p) (3d) (4s,4p) (4d) (4f) (5s,5p)
2) Any electrons to the right of the electron of interest contributes no shielding. (Approximately correct statement.)
3) All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charge units[ for 1s^2 only ;many books take 0.30]
4) If the electron of interest is an s or p electron: All electrons with one less value of the principal quantum number shield to an extent of 0.85 units of nuclear charge. All electrons with two less values of the principal quantum number shield to an extent of 1.00 units.
5) If the electron of interest is an d or f electron: All electrons to the left shield to an extent of 1.00 units of nuclear charge.
6) Sum the shielding amounts from steps 2 through 5 and subtract from the nuclear charge value to obtain the effective nuclear charge.
Taking an example of Fe :
(1s2)(2s2,2p6)(3s2,3p6) (3d6) (4s2)
For 4s[ 26th electron]
0.35.1+0.85.14+10.1=0.35+11.90+10=22.25;Zeff= 26-22.25=3.75
For 3d[24th electron]
0.35 • 5 + 1.18==19.75; Zeff=26-19.75 =6.25
For 3p[ 18th electron]
0.35.7+0.85.8+1.2= 11.25; Zeff= 26-11.25=14.75
For 2p[ 8th electron]
0.35.7+0.85.2=2.45+1.70=4.15; Zeff= 26-4.15=21.85
For 1s[ 2nd electron]
0.30.1= 0.30; Zeff= 26-0.30= 25,70
3.75[ 26th ]4.10 [25th ]6.25[24th ],7.25[23th],8.25[22th],9.25[21th],10.25[20th ]11.25[19th ] 14.75[18th],15.4 [17th] ,16.05[16th],16.7 [15th],-17.35 [14th] 18[13th] 14.85[12th] and so on you calculate Z* for all the 26 electrons of Fe.
For your verification / authentication, pls find an attachment.
Manohar Sehgal : Respected sir, i understand it very well. But my point is, if i take the average of 1s, 2s, 2p, 3s, 3p, 3d electron's effective nuclear charge, then I will get another number (answer is 15.59 for Fe). Is there any significance exits for this number ?
Best of my knowledge, this term is not reported yet. During curve fitting of data, i am getting a number for different systems e.g. Fe, Ni, Br and V. when i cross check the term for effective nuclear charge it was showing wrong result, but average of all the effective nuclear charges matches very well with this term. If you have any guess, please send me. Thanx
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Atomic, Molecular and Optical Physics