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AP Chemistry · Unit 1: Topics 1.6–1.8 Master Companion

⚛️ Topic 1.6 Guide 📊 Topic 1.7 Guide 🧪 Topic 1.8 Guide 📺 Slides
Week 5 Master Companion Jeremy Krug Curriculum 12 Worked Walkthrough Models

Photoelectron Spectroscopy, Periodic Trends & Ionic Bonding

Unit 1: Topics 1.6, 1.7 & 1.8 · Official Student Revision Packet & Homework Companion
Course: AP Chemistry Teacher: Mr. Hisham Mahmoud / Jeremy Krug Platform: SABIS-CHEMISTRY.COM Unit: Unit 1 (Atomic Structure & Properties)
📑 Dedicated Standalone Guides (Topics 1.6, 1.7 & 1.8)
Need to focus on a single subtopic? Access and print our three standalone topic companions below:
⚛️ Topic 1.6 Guide: PES Photoelectron Spectroscopy physics, backwards x-axis rule, peak heights, core shifts & subshell evidence.
Open Topic 1.6 Guide ↗
📊 Topic 1.7 Guide: Periodic Trends Coulomb's Law, atomic & ionic radii, isoelectronic series, Be/B & N/O exceptions & successive IE tables.
Open Topic 1.7 Guide ↗
🧪 Topic 1.8 Guide: Ionic Bonding Valence electrons, Transition metal FIFO rule, 3D crystal lattices, empirical formulas & 2-step lattice energy.
Open Topic 1.8 Guide ↗

⚡ Topic 1.5 Prerequisite Architecture: Orbitals & Periodic Blocks

Slide 1.5 Review

Interpreting PES spectra (Topic 1.6) and periodic trends (Topic 1.7) builds directly upon orbital filling and periodic block architecture from Topic 1.5:

Periodic Table Block Architecture (s, p, d, f)
Topic 1.5 Architecture: Periodic Table Blocks ($s$, $p$, $d$, $f$) and valence subshell configurations.
Aufbau Diagonal Filling Order Ladder
Topic 1.5 Filling Order: Aufbau diagonal ladder ($1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d$).

Topic 1.6: Photoelectron Spectroscopy (PES)

Niels Bohr modeled electrons in concentric circular shells ($n = 1, 2, 3$). If the Bohr model were complete, all electrons in shell $n = 2$ would have identical energies. PES experimentally disproved this: $n = 2$ electrons require two distinct ionization energies, proving the existence of $2s$ and $2p$ subshells.

Jeremy Krug's Golden PES Rule
The horizontal axis runs BACKWARDS! High binding energy is on the far left (closest to nucleus). Low binding energy is on the far right (valence electrons).
Neon PES Spectrum
Figure 1.6-1 (From AP 1.6 Slide 14): Neon PES Spectrum ($1s^2 2s^2 2p^6$) — 3 peaks with height ratios 1:1:3.
Hydrogen vs Helium PES Spectra
Figure 1.6-2 (From AP 1.6 Slide 11): H vs. He — Helium holds 2 electrons (twice height) and 2 protons (shifted left).
Core 1s Shift in Nitrogen vs Oxygen
Figure 1.6-3 (From AP 1.6 Slide 17): Core 1s Peak Shift — Oxygen ($Z=8$) exerts stronger nuclear pull than Nitrogen ($Z=7$), shifting its $1s$ peak left to higher binding energy.

Topic 1.7: Periodic Trends & Coulomb's Law

The Cardinal Rule for Free Response Questions
NEVER justify a periodic trend by citing its position on the periodic table ("because it is higher and to the right" = 0 points on the AP Exam). ALWAYS explain using:
  1. Distance ($r$) / Number of Shells: Dominates down a group ($F \propto 1/r^2$).
  2. Effective Nuclear Charge ($Z_{\text{eff}}$): Dominates across a period ($Z_{\text{eff}} \approx Z - S$).
Periodic Trends across Periods and Groups
Figure 1.7-1 (From AP 1.7 Slide 5): Periodic Trends Summary Map — Atomic radius increases down and left; Ionization energy and Electronegativity increase up and right.
First Ionization Energy of the Elements Graph
Figure 1.7-2 (Wikimedia Commons): First Ionization Energy vs. Atomic Number ($Z$). Note drops at Be $\rightarrow$ B ($2s \rightarrow 2p$) and N $\rightarrow$ O (pairing repulsion).
Periodic Trend Across a Period ($\rightarrow$) Down a Group ($\downarrow$) Coulombic Justification
Atomic Radius Decreases Increases Across: $Z_{\text{eff}}$ increases, pulling shell tighter.
Down: Additional energy levels place valence electrons at larger $r$.
1st Ionization Energy Increases Decreases Across: Higher $Z_{\text{eff}}$ binds valence electrons tighter.
Down: Greater distance $r$ and core shielding weaken nuclear pull.
Electronegativity Increases (up to F = 4.0) Decreases Across: Nucleus draws shared bond pairs closer.
Down: Shared electrons are farther from nucleus and shielded.
Ionic Radius Cations < Parent
Anions > Parent		 Increases Cations lose valence shell; reduced repulsion.
Anions gain electrons; increased repulsion inflates cloud.

Topic 1.8: Valence Electrons, Ionic Compounds & Lattice Energy

The Transition Metal FIFO Rule

When transition metals form cations, electrons are removed from the highest principal quantum level ($4s$) before $3d$:

  • $\text{Fe}: [Ar] 4s^2 3d^6$
  • $\text{Fe}^{2+}: [Ar] 3d^6$   (Loses the two 4s electrons!)
  • $\text{Fe}^{3+}: [Ar] 3d^5$   (Loses two 4s electrons plus one 3d)
Transition Metal Cation Stripping Table
Figure 1.8-1 (From AP 1.8 Slide 7): Transition Metal 4s Stripping Order — Outer $4s$ emptied before $3d$.
Ionic Lattice Coulombic Forces
Figure 1.8-2: Coulombic Forces in Ionic Lattices — $F \propto \frac{|q_1 \cdot q_2|}{r^2}$.
Sodium Chloride 3D Crystal Lattice
Figure 1.8-3 (Wikimedia Commons): 3D alternating ionic crystal matrix of $\text{NaCl}$.
Halite Cubic Crystal Cleavage
Figure 1.8-4 (Wikimedia Commons): Natural cubic cleavage of $\text{NaCl}$ under shear impact.

Jeremy Krug's 2-Step Lattice Energy Protocol

Lattice Energy $\propto \frac{|q_1 \cdot q_2|}{r}$
  1. Step 1: Check Charge Magnitude First ($|q_1 \cdot q_2|$): Charge product is KING! $\text{MgO}$ ($|(+2)(-2)| = 4$) has $\approx 4\times$ greater lattice energy and a much higher melting point ($2852^\circ\text{C}$) than $\text{NaCl}$ ($|(+1)(-1)| = 1$, $801^\circ\text{C}$).
  2. Step 2: Check Ionic Radius as a Tiebreaker Only ($r$): When charges match (e.g. $\text{NaF}$ vs $\text{NaCl}$ vs $\text{NaBr}$), smaller ions pack closer together, yielding stronger lattice energy: $\mathbf{\text{NaF} > \text{NaCl} > \text{NaBr}}$.

Topic 1.6: Photoelectron Spectroscopy (PES) In-Depth

Open Full Standalone 1.6 Guide ↗

Monochromatic photons of known energy strike gaseous atoms. Kinetic energy is measured to calculate binding energy: $E_{\text{photon}} = \text{BE} + \text{KE}$.

  • Peak Position: Tells which subshell the electrons occupy. $1s$ is always on the far left.
  • Peak Height: Proportional to electron count ($s=2, p=6, d=10$).
  • Core Shifts: Higher atomic number ($Z$) pulls inner $1s$ electrons tighter, shifting the peak further left ($239\text{ MJ/mol}$ for S vs $178\text{ MJ/mol}$ for Si).
Neon PES Spectrum
AP 1.6 Slide 14: Neon PES Spectrum — 1:1:3 ratio for $1s^2, 2s^2, 2p^6$.
Hydrogen vs Helium PES Spectra
AP 1.6 Slide 11: Hydrogen vs Helium — Peak height and nuclear charge shift.

Topic 1.7: Periodic Trends & Coulombic Mechanics

Open Full Standalone 1.7 Guide ↗

All trends rely on Coulomb's Law ($F \propto \frac{q_1 q_2}{r^2}$).

The Two Major AP Ionization Energy Anomalies:

  • Be vs B: Boron's $2p^1$ electron is in a higher-energy subshell shielded by $2s^2$, so its IE₁ is lower than Beryllium's full $2s^2$.
  • N vs O: Oxygen's fourth $2p$ electron must pair up in an orbital ($\uparrow\downarrow \ \uparrow \ \uparrow$). Localized electron-electron repulsion destabilizes it, lowering its IE₁ compared to Nitrogen's half-filled $2p^3$.

Isoelectronic Series:

$\text{O}^{2-} (8p) > \text{F}^- (9p) > \text{Na}^+ (11p) > \text{Mg}^{2+} (12p) > \text{Al}^{3+} (13p)$. More protons with identical shielding = smaller radius.

Periodic Trends Summary Map
AP 1.7 Slide 5: Periodic Trends Summary Vector Map across Periods and Groups.

Topic 1.8: Valence Electrons, Ionic Compounds & Lattice Energy

Open Full Standalone 1.8 Guide ↗

Ionic solids form continuous 3D lattices. There are NO individual molecules of $\text{NaCl}$.

Physical properties: High melting points due to strong Coulombic attraction; brittle because shear force aligns like charges which repel and cleave; non-conductive as solids but highly conductive when molten or dissolved in water.

Transition Metal Configurations: Neutral vs Cations
AP 1.8 Slide 7: Transition Metal 4s Stripping Order — Cations lose outermost $4s$ electrons first.

12 Complete Worked AP Walkthrough Models

Model 1: Deducing Unknown Element from Multi-Peak PES Spectrum Topic 1.6

Peaks at $104\text{ MJ/mol}$ (ht 2, $1s^2$), $6.84\text{ MJ/mol}$ (ht 2, $2s^2$), $3.67\text{ MJ/mol}$ (ht 6, $2p^6$), and $0.50\text{ MJ/mol}$ (ht 1, $3s^1$). Total electrons = 11 $\rightarrow$ Sodium ($\text{Na}$).

Model 2: Core Peak Shifts (Sulfur vs. Silicon) Topic 1.6

Both S ($Z = 16$) and Si ($Z = 14$) have two $1s$ electrons. Sulfur has 16 protons vs 14 in Silicon. By Coulomb's Law, the greater nuclear charge in Sulfur holds $1s$ electrons tighter $\rightarrow$ higher binding energy ($239$ vs $178\text{ MJ/mol}$).

Model 3: PES Peak Heights of Nitrogen vs. Oxygen Topic 1.6

Nitrogen has 7 electrons ($1s^2 2s^2 2p^3$); Oxygen has 8 electrons ($1s^2 2s^2 2p^4$). Oxygen's $2p$ peak is $4/3\times$ taller than Nitrogen's, and all of Oxygen's peaks are shifted to the left (higher binding energy) due to $+1$ proton.

Model 4: Transition Metal PES Order (Scandium, Z = 21) Topic 1.6

Scandium configuration: $1s^2 2s^2 2p^6 3s^2 3p^6 3d^1 4s^2$. In PES, the $3d$ peak appears to the left of $4s$ (higher binding energy). Once populated, $3d$ electrons are closer to the nucleus on average, which is why $4s$ electrons are ionized first.

Model 5: Explaining Atomic Radius Contraction Across Period 3 Topic 1.7

From Na to Cl, valence electrons enter the same shell ($n = 3$) with constant core shielding. Nuclear charge increases from $+11$ to $+17$, pulling electrons closer $\rightarrow$ atomic radius decreases.

Model 6: Isoelectronic Radius Ranking ($\text{O}^{2-}, \text{F}^-, \text{Na}^+, \text{Mg}^{2+}, \text{Al}^{3+}$) Topic 1.7

Ranking: $\mathbf{\text{O}^{2-} > \text{F}^- > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}}$. All have 10 electrons. Aluminum has 13 protons exerting the strongest Coulombic pull on the identical electron cloud, producing the smallest radius.

Model 7: Ionization Energy Anomaly: Beryllium vs. Boron Topic 1.7

Boron ($2p^1$) has a lower IE₁ than Beryllium ($2s^2$) because the $2p$ subshell is higher in energy and partially shielded by the inner $2s^2$ electrons.

Model 8: Ionization Energy Anomaly: Nitrogen vs. Oxygen Topic 1.7

Oxygen has lower IE₁ than Nitrogen because removing an electron from Oxygen relieves localized electron-electron repulsion between the paired electrons in its $2p^4$ orbital.

Model 9: Deducing Unknown Element and Formula from Successive IE Table Topic 1.7

IE jumps from $4356\text{ kJ/mol}$ ($\text{IE}_4$) to $16091\text{ kJ/mol}$ ($\text{IE}_5$). Giant jump at $\text{IE}_5$ proves 4 valence electrons (Group 14, Period 3 = $\text{Si}$). Compound with chlorine is $\mathbf{\text{SiCl}_4}$.

Model 10: Transition Metal FIFO Electron Configurations Topic 1.8

Neutral Iron ($\text{Fe}$): $[Ar] 4s^2 3d^6$. When forming $\text{Fe}^{2+}$, the two $4s$ electrons are removed first: $\mathbf{\text{Fe}^{2+} = [Ar] 3d^6}$. For $\text{Fe}^{3+}$, an additional $3d$ electron is removed: $\mathbf{\text{Fe}^{3+} = [Ar] 3d^5}$.

Model 11: Comparing Melting Points: Charge Product Dominance ($\text{CaO}$ vs $\text{KF}$) Topic 1.8

$\text{CaO}$ has $+2/-2$ ions ($|q_1 q_2| = 4$) while $\text{KF}$ has $+1/-1$ ions ($|q_1 q_2| = 1$). Fourfold greater charge product results in far stronger lattice energy $\rightarrow$ melting point of $\text{CaO}$ ($2572^\circ\text{C}$) is much higher than $\text{KF}$ ($858^\circ\text{C}$).

Model 12: Comparing Lattice Energy: Internuclear Distance Tiebreaker Topic 1.8

Comparing $\text{NaF}, \text{NaCl}, \text{NaBr}$: all have $+1/-1$ charges. Anion radius increases down Group 17 ($\text{F}^- < \text{Cl}^- < \text{Br}^-$). Smaller distance $r$ gives stronger Coulombic attraction: $\mathbf{\text{NaF} > \text{NaCl} > \text{NaBr}}$.

AP Chemistry Trap & Misconception Matrix

Frequent Exam Mistake Why It Loses Points The AP-Accurate Correction
"IE increases because it's further right." Table position is not a physical mechanism. Cite increasing effective nuclear charge ($Z_{\text{eff}}$) pulling on electrons in the same principal energy level.
"PES peak height shows electron energy." Confuses the vertical axis (count) with horizontal (energy). Peak height represents number of electrons in that subshell. Peak position on x-axis represents binding energy.
"NaCl is a molecule." Ionic solids do not form discrete covalent molecules. Ionic compounds form continuous 3D crystalline lattices of formula units.
"Iron(II) ion is $[Ar] 4s^2 3d^4$." Fails to apply the FIFO rule. Electrons in highest principal level ($4s$) are always stripped before $3d$ ($\text{Fe}^{2+} = [Ar] 3d^6$).
"Size decides lattice energy before charge." Charge product ($q_1 q_2$) has far greater mathematical impact than size differences. Always check ion charge product first ($+2/-2 > +1/-1$). Use radius only as a secondary tiebreaker.
SABIS Chemistry · Official AP Chemistry Learning Catalogue · Unit 1 Companion Series