Answers to Exercises on “Using the Shell Model to Predict Periodic Properties”
Worksheet
Exercises:
1.
2.
3.
4.
5.
Calculate the Zeff of the (outer electron(s) in the) following: Li, C, S, Ar, Cl, Cl-, Cl+, Ca, Ca+, Ca2+
Which is larger, Cl or Cl-? Which is larger, Cl or Cl+?
Consider Ca, Ca+, Ca2+ Which has the greatest ionization energy? The greatest radius?
Consider Na+, Mg+, Al+ Which has the smallest ionization energy? The smallest radius?
Consider Na+, Ne, and F- Which has the greatest ionization energy? The greatest radius?
(Note: The species in #5 above are called "isoelectronic" species because they have the same number of
electrons. Zumdahl does a nice job discussing these, although they do so without using Zeff directly.)
-----------------------------------------------------------Answers:
1. Using the "simple" equation (model) for Zeff, you'd get (for the outermost electrons in each):
Electron Configuration
Species
Zeff*
(shielding electrons/sublevels
blue-bolded)
Li
1s22s1
+3 -2 = +1
C
1s22s22p2
+6 - 2 = +4
S
1s22s22p63s23p4
+16 - 2 - 8 = +6
Ar
1s22s22p63s23p6
+18 - 2 - 8 = +8
Cl
1s22s22p63s23p5
+17 - 2 - 8 = +7
Cl1s22s22p63s23p5
+17 - 2 - 8 = +7
Cl+
1s22s22p63s23p5
+17 - 2 - 8 = +7
Ca
1s22s22p63s23p64s2
+20 - 2 - 8 - 8 = +2
Ca+
1s22s22p63s23p64s2
+20 - 2 - 8 - 8 = +2
2+
Ca
1s22s22p63s23p6
+20 - 2 - 8 = +10
*NOTE: The Zeff is equal to the group number only if the species is a (neutral) atom!!!
2. Cl- is larger than Cl, because although Cl- and Cl have the same apparent Zeff (in the simple model—
See Q1), there is one extra electron in Cl-, and so there is a much greater amount of electron-electron
repulsion, and so the electrons will be repelled more and pushed farther away from the nucleus
(anion expands vs. neutral atom).
Cl is larger than Cl+, because although they have the same apparent Zeff (in the simple model), there is
one fewer electron in Cl+, and so there is a much smaller amount of electron-electron repulsion, and
so the electrons will be repelled less and pulled closer in toward the nucleus (cation contracts vs.
neutral atom).
3. Ca2+ has the greatest ionization energy BY FAR!!! The Zeff for Ca2+ is +10 (see Q1), which is 5 times
greater than the Zeff of the other two, so it will be much harder to remove an outer electron from Ca2+
than the other two. (Note: The electron being removed from Ca2+ is coming from the n = 3 level [so
there are only 10 shielding electrons], whereas the outer electron in Ca+ or Ca is coming from the n =
4 level [where there are now 18 shielding electrons, making Zeff much smaller])
Ca has the greatest radius. It has the same apparent Zeff (in the simple model) as Ca+, but there is one
more e- in Ca than Ca+ which means more electron-electron repulsion in Ca, making it larger. Note:
ionization energy and radius tend to have opposite trends.
4. Note: The electron configurations are: Na+: 1s22s22p6;
The Zeff for (the outermost e- in) Na+ is +11 - 2 = +9;
for Mg+ , Zeff = +12 -2 -8 = +2;
for Al+, Zeff = +13 - 2 - 8 = +3
Mg+: 1s22s22p63s1;
Al+: 1s22s22p63s2
Answers to Exercises on “Using the Shell Model to Predict Periodic Properties”
Worksheet
Thus the one with the greatest ionization energy, BY FAR, is Na+; next is Al+, and Mg+ has the
smallest.
Na+ has the smallest radius for similar reasons. Although it’s true that Na+ has its outer electrons in a
lower-energy “shell” (n = 2 vs n = 3), even if that weren’t the case, you’d argue it must be much smaller
because of the MUCH GREATER effective nuclear charge “seen” by its outermost electrons.
5. Note: The electron configurations are: Na+: 1s22s22p6;
Ne: 1s22s22p6;
F-: 1s22s22p6
Each species has 10 electrons, but the number of protons is different! This affects Zeff:
The Zeff for (the outermost e- in):
Na+ is
Ne is
F- is
+11 - 2 = +9;
+10 - 2 = +8;
+9 - 2 = +7
Thus, Na+ has the greatest ionization energy (and smallest radius),
and F- has the greatest radius (and lowest ionization energy)