Slater s rules 1,2,3,4

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1 Slater s rules 1,2,3,4 Slater s rules are a guideline for determining shielding and, therefore, Z eff. The rules are best used for atoms with n > 1. Remember, when we wish to determine or conceptualize Z eff, we are considering only one of the outer most electrons. We are interested in the electron with the highest energy (n,l) as the electron that is being shielded by the other electrons in the atom. For example, a sodium atom has 11 electrons, but 10 of those electrons are shielding the outermost electron in the highest n,l. This means that all of the electrons in n= 1, and n=2 shield the electron in 3s for sodium from the nucleus, with the 1 s electrons being more effective at shielding than the 2s and 2p electrons. Electrons with the same n and l as the electron of interest are not as good at shielding that electron as inner electrons of n-1, or smaller n s. Of course, electrons closest to the nucleus shield the best. How can we use the Slater s Rules and Z eff? Slater s rules help us conceptualize trends. Consider the lithium atom. Lithium has an IE 1 =520kJ/mol, while the IE 1 for hydrogen is 1310kJ/mol. This means one needs more energy to remove an electron from the hydrogen atom then one needs for the same process for lithium. The average radius for lithium is larger than that of hydrogen. Therefore, the outer electron is further from the nucleus for lithium because that electron is a 2s orbital. Inner core electrons repel the electron of interest, the 2s 1 electron, so it does not penetrate the nucleus effectively. Therefore, this electron is easily removed. Most of the 1s electrons density is very close to the nucleus. The electron of interest has a Z eff of 1.3 based on Slater s Rules. This concedes with computer simulations of the radius. The radial distribution of the 2s orbital shows that it can penetrate to the nucleus-just not very well. Rules to determine shielding based on Slater s values: 1. Write the electron configuration for the atom based on the order of the periodic table 1 ssrules.htm 2 Ref: 3 srule.html 4 J.C. Slater s, phys Rev1930, v36,p57 pinar m alscher Page 1 of 9 4/28/15

2 2. Put that configuration in energy order 3. Group electron configurations by n value 4. (1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5d)(5d)(5f) 5. For ns, or np electrons: 6. Electrons in the same group shield 0.35, Except 1s, which shields 0.30 for H and He only. 7. When n=2, we use 0.35 for the 1s electrons 8. Electrons in the n-1 group shield Electrons in the n-2 group shield Electrons in nd or nf shield Assign any electrons to the left of the d or f electrons 1.00 A general equation: S = 1.00n n n n n 0. 5 n 0 is the energy level where the electron of interest is housed. n n-1 is one shell less; n n-2 is any other core electrons. For Example, an electron is in n=4 shell. n 0 refers to n=4, n n-1 refers to n=3, while n n-2 refers to n= 2 and n= 1 shells. Electrons to the right of the electron of interest do not shield. EXAMPLE 1: 2p electron in fluorine Fluorine. 1s 2 2s 2 2p 5 (1s) 2 (2s,2p) 7-1 Explanation of values: There are 2 electrons in n=1. There are 7 e in n=2 but this includes the electron of interest so, subtract 1 leaving 6 electrons that we count in n=2, because an electron does not shield it's self. There aren t any n-2 electrons. S = 1.00n n n n n 0 S = 2 x x 0.35 = 3.8; 9-3.8=5.2. The Z eff that the outer most electron of fluorine feels is 5.2, much lower than the +9 charge. EXAMPLE 2: 4s electron in calcium 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 (1s) 2 (2s,2p) 8 (3s,3p) 8 (4s,4p) 2-1 S = 1.00n n n n n 0 2 x x x x 0.35 =17.15; = Similar calculators can be found on line. They are good for checking work, but of little use during a test. Here is one such calculator:http://calistry.org/calculate/slaterrulecalculator pinar m alscher Page 2 of 9 4/28/15

3 The Z eff of Ca is 2.85 Explanation of values: Calcium has 10 electrons that are considered inner core, n-2 or lower in energy. These are the 2 electrons from n=1, and 8 electrons from n=2. There are 8 electrons from n=3, but these are n-1, so count for 0.85 shielding. 4s has two electrons (it s calcium!), but we consider only 1 of these electrons at 0.35 shielding. EXAMPLE 3: a 4s electron in scandium 1s 2 2s 2 2p 6 3s 2 3 p 6 4s 2 3d 1 Write in energy order 1s 2 2s 2 2p 6 3s 2 3p 6 3d 1 4s 2 (1s) 2 (2s,2p) 8 (3s,3p) 8 (3d) 1 (4s,4p) 2-1 S = 1.00n n n n n 0 2 x x x 0.85 [b/c 8 n=3 e in 3s and 3p and 1 in 3d] +1 x 0.35=18; 21-18=3 For most transition metals, nd >ns or np, in the Slater s rules, and nd electrons are considered inner core electrons. Sc is the odd ball. The nuclear pull is about the same for 3d as for 4s EXAMPLE 4: 4s for Cu vs. 3d for Cu 4s for Cu 1s 2 2s 2 2p 6 3s 2 3 p 6 4s 1 3d 10 Write in energy order 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 (1s) 2 (2s,2p) 8 (3s,3p) 8 (3d) 10 (4s,4p) 1-1 S = 1.00n n n n n 0 S = 2 x x x x x 0.35 =25.3 Z eff = =3.70 3d for Cu 1s 2 2s 2 2p 6 3s 2 3 p 6 4s 1 3d 10 Write in energy order 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 1 (1s) 2 (2s,2p) 8 (3s,3p) 8 (3d) 10-1 (4s,4p) 1 S = 2 x x x x 0.35+ignore 4s= = 7.85 pinar m alscher Page 3 of 9 4/28/15

4 Explanation of values: Copper has 10 electrons that are considered inner core, n-2 or lower in energy. These are composed of the 2 electrons from n=1, and 8 electrons from n=2and are the same for any outer electron for copper. We find differences in values when we look at the electron shielding in different higher energy orbitals on the copper atom. Lets look at the electron in the 4s orbital. It is shield by everything in n=3. The 8 electrons from 3s and 3p and the 10 electrons from 3d comprise the 18 electrons that are shielding at There is one electron in 4s, so it does no shielding (it can t shield itself). Contrast this with an electron in 3d. 9 other electrons in the same sub shell shield the 3d electron. The other electrons shield these extremely well, and are give a value of The 4s electron does not shield the 3d electrons; it is higher in energy. The 3 electron has a stronger attraction to the nucleus than the 4s electron. The Z eff is higher; a stronger attraction means it takes more energy to remove that electron. The electron that is removed for ionization must come from 4s 5. Cations and anions shielding work in a similar manner. EXAMPLE 5:6s electron in platinum 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 1 4f 14 5d 9 (1s) 2 (2s,2p) 8 (3s,3p) 8 (3d) 10 (4s, 4p) 8 (4d) 10 (4f) 14 (5s,5p) 8 (5d) 9 (6s) x x x x x x x x 17 =74.45 Z eff = =3.55 Explanation of values: Platinum has a lot of electrons. Consider the outer electrons first. The electron of interest is in the 6s orbital. The energy shell below that is n=5. There are 16 electrons in n= 5; the electrons in n=4 and lower shield by EXAMPLE 6: 1s electron in Os Os: (1s) 2 (2s2p) 8 (3s3p) 8 (3d) 10 (4s4p) 8 (4d) 10 (4f) 14 (5s5p) 8 (5d) 6 (5f) 0 (6s6p) 2 For the 1s valence electron: S = (1)(0.30)+the rest don t matter since they don t shield) so Z eff = = 75.7 The 1s electrons are poorly shielded. It will be very difficult to remove an pinar m alscher Page 4 of 9 4/28/15

5 electron from the 1s orbital. PROBLEMS 1. Write the electron configuration for P, F, Cl, Mg, and C, then group the s and p electrons together, by n values. P 1s 2 2s 2 2p 6 3s 2 3p 3 ;(1s) 2 (2s2p) 8 (3s3p) 5 F Cl Mg C 2. Write the electron configuration by groupings using the Slater equation. P 1s 2 2s 2 2p 6 3s 2 3p 3 ;(1s) 2 (2s2p) 8 (3s3p) 5-1 F Cl Mg C 3. Determine Slater s shielding value for each of the elements and the Z eff. P S = 2x x x 0.35 = 10.2; = 4.8 F pinar m alscher Page 5 of 9 4/28/15

6 Cl Mg C 4. We are interested in the behavior of outer core electrons, but we can use Slater s Rules for any electron. As seen in the rules, electrons that are in orbitals that are after the electron of interest do not contribute to the shielding of that electron. Determine the S and Z eff for each of the following. 2s electron in P 1s 2 2s 2 2p 6 3s 2 3p 3 ;(1s) 2 (2s2p) 8-1 (3s3p) 5-1 S = 2x x 0.85 = = p electron in Mg 2s electron in Cl 1s electron in He (follow the steps!) 1s electron in Mg 5. Cations and anions: follow the rules! 2s electron in Na + 1s 2 2s 2 2p 6 3s 1 ;(1s) 2 (2s2p) 8-1 (3s3p) 0 S = 2x x 0.85 = = p electron in Cl 2p electron in Mg 2+ 1s electron in Li + (follow the steps!) pinar m alscher Page 6 of 9 4/28/15

7 6. Transition elements: reviewing the rules: electrons in the same (nd) group contribute 0.35 towards the overall shielding. s in all groups to the left in the Slater configuration format contribute 1.00 towards overall shielding. Electrons in all groups to the right in the slater configuration contribute notheing towards overall shielding. A 3d electron in Ni 1s 2 2s 2 2p 6 3s 2 3p 6 3d 8 4p 2 ;(1s) 2 (2s2p) 8- (3s3p) 8 (3d) 8-1 (4s) 2 ; S = 18x1.00+7x0.35=20.45; =7.55 3d electron in Mn 4d electron in Ru Using the techniques above, give a reason why the following occurs: 7. The radius of Cd 2+ is smaller than that of Sr 2+. Calculate the Z eff for the outer most orbital for each atom and each ion. Calculate the Z eff for a 3s orbital for each atom. Give a rational explanation for your findings. 8. The ionization potentials increase subtly for Ru and Rh and have a large increase for Pd, but decrease in the series Fe, Co, Ni. The electron of interest is in the 5s orbital for Ru, Rh, and 4d orbital for Pd (4d because 5s is empty), and 4s for Fe, Co, and Ni kj x mol -1 Ru kj x mol -1 Rh kj x mol -1 Pd kj x mol -1 Fe kj x mol -1 Co kj x mol -1 Ni 9. Consider the melting point data for the natural forms of the second row elements. Calculate Z eff using Slater's rules for the outermost electron for each of these elements. Does Z eff give a reasonable accounting of the trend in the melting point? Why or why not? Should melting point be considered a periodic property of atoms? Why or why not? Melting Point ( C) Na 98 Mg 650 pinar m alscher Page 7 of 9 4/28/15

8 Al 660 Si 1414 P 44 S 115 Cl Ar Calculate Z eff for the highest energy electron in the following ions: K +, Ca +, Sc +, Ti +, V +. Does Z eff account for the observed values of the second ionization potential of these elements? Why or why not? Some have argued that Ca + should be considered a transition metal. Give an argument to support this contention. 11. Look at a plot for the electron affinity as a function of atomic number for the atoms from Li to Ne. In general, does Z eff account for the variation in electron affinity? Why or why not? Are there any specific anomalies in the trend? If so, give an explanation. PS-Would I ask this on a test. How about an answer with no hedging, maybemaybe not. You should be able to do the examples and read through the problem answers with a nod of the head and a, hmmm, I think I get it!. think about how you might summarize the answer. [oh and I have asked #1 on a test!] pinar m alscher Page 8 of 9 4/28/15

9 pinar m alscher Page 9 of 9 4/28/15

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