SME
General Chemistry I · Problem type
Effective nuclear charge (Slater’s rules)
Use this for “Use Slater’s rules to find the effective nuclear charge on a 2p electron of nitrogen.”
Diagram
7 electrons (Nitrogen): [He] 2s² 2p³.
Boxes fill from the lowest energy up; each box of a subshell takes one arrow before any takes two, and two arrows in a box point opposite ways.
Unpaired electrons (single arrows, lit): 3.
This is an example. Type your own values to start a new problem.
S
=
0.35
×
a
+
0.85
×
b
+
1.00
×
c
Zeff
=
Z
−
S
Formulas
S
=
0.35
×
a
+
0.85
×
b
+
1.00
×
c
3.1 = 0.35 × 4 + 0.85 × 2 + 1.00 × 0
Zeff
=
Z
−
S
3.9 = 7 − 3.1
Assumptions
•
Slater’s rules for one s or p electron with n ≥ 2: each other electron in its (ns, np) group shields 0.35, each in shell n − 1 shields 0.85, each deeper one 1.00.
•
Shell n − 1 counts all its s, p and d electrons. A 1s electron’s partner shields 0.30, and d and f electrons follow other rules.
•
A higher Zeff pulls the electron closer and holds it harder, so radii shrink and ionization energies rise across a period.
Step-by-step
WE KNOW
Z = 7, a = 4, b = 2, c = 0
FIND
shielding constant (S), effective nuclear charge (Zeff)
Step 1 · Find shielding constant (S)
Use S = 0.35 × a + 0.85 × b + 1.00 × c
Slater: weight each group’s electrons by how well they shield, then add.
S
=
0.35
×
4
+
0.85
×
2
+
1.00
×
0
S
=
1.4
+
1.7
S
=
3.1
Step 2 · Find effective nuclear charge (Zeff)
Use Zeff = Z − S
The electron feels the protons less the charge the others screen off.
Zeff = 7 − 3.1
Zeff = 3.9
Check
Put the numbers back in. Both sides should match.
3.1 = 0.35 × 4 + 0.85 × 2 + 1.00 × 0 ✓
3.9 = 7 − 3.1 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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