Questions: Periodic Table and Orbital Filling Rules

Question 1

Period 4 of the periodic table has 18 elements. Which sequence of subshells is filled across period 4, and why does this produce exactly 18 elements?

• A. 4s, 4p, 4d — three subshells with 2, 6, 10 electrons = 18
• B. 4s, 3d, 4p — filling 4s (2 electrons), then 3d (10 electrons), then 4p (6 electrons) = 18 elements
• C. 3d, 4s, 4f — these three subshells together hold 18 electrons
• D. 4s, 4p — two subshells each with 9 electrons give 18 total

Answer: (B)

Period 4 begins with 4s (2 electrons: K and Ca), then fills the 3d subshell (10 electrons: the transition metals Sc through Zn), then fills 4p (6 electrons: Ga through Kr). The count is 2 + 10 + 6 = 18. The 3d fills within period 4 rather than period 3 because in multi-electron atoms the 4s orbital is lower in energy than 3d during filling, so potassium puts its 19th electron into 4s. Once 4s is filled, 3d fills before 4p as the next available subshell by energy.

Question 2

Potassium (element 19) places its 19th electron in the 4s orbital rather than 3d. Which best explains why?

• A. The 3d subshell is completely full in period 3, leaving no room for potassium's electron
• B. In multi-electron atoms, the 4s orbital has lower energy than 3d during filling due to electron penetration effects, so the aufbau principle dictates filling 4s first
• C. Potassium is an alkali metal by definition, and alkali metals always have electrons in s-orbitals
• D. The Pauli exclusion principle prevents any electron from occupying 3d until 3s and 3p are completely filled

Answer: (B)

In multi-electron atoms, electron-electron repulsion and nuclear shielding shift orbital energies relative to the hydrogen-like case. The 4s orbital penetrates closer to the nucleus than 3d (higher electron density near the origin), experiencing stronger nuclear attraction and sitting at lower energy during filling. So the aufbau principle places the 19th electron in 4s, giving potassium alkali-metal character. Once 3d is filled, it can drop below 4s in energy, which is why transition metals lose their 4s electrons first in ionization.

Question 3

Most elements in the same column of the periodic table have identical electron configurations.

• T. True
• F. False

Answer: False

Elements in the same column share the same valence electron configuration — the outermost electrons that determine chemical behavior — but their complete configurations differ. Sodium (Na, period 3) is [Ne] 3s¹ and potassium (K, period 4) is [Ar] 4s¹: both have a single valence s-electron but different core electrons and principal quantum numbers. It is the shared valence configuration, not the total configuration, that gives column-mates similar chemical properties.

Question 4

The periodic table's row lengths — 2, 8, 8, 18, 18, 32 — directly reflect the number of available electron states in each period's filling sequence, derived from quantum mechanical counting of orbitals.

• T. True
• F. False

Answer: True

Each subshell holds 2(2ℓ+1) electrons: s holds 2, p holds 6, d holds 10, f holds 14. Period 1: only 1s → 2 elements. Periods 2 and 3: s and p → 8 elements each. Periods 4 and 5: s, d (from the previous shell), p → 18 elements each. Periods 6 and 7: s, f, d, p → 32 elements each. The periodic table's dimensions are not an empirical discovery but a direct read-off of quantum mechanical state counting under the Pauli exclusion principle.

Question 5

Explain why sodium (Na, period 3) and potassium (K, period 4) have similar chemical properties despite being in different periods with different total numbers of electrons.

Model answer: Chemical behavior is determined primarily by valence electrons — the outermost, most loosely bound electrons that participate in bonding. Sodium has the configuration [Ne] 3s¹ and potassium [Ar] 4s¹: both have a single valence electron in an s-orbital, one beyond a complete noble-gas core. This shared valence structure means both readily lose one electron to form +1 ions and share the same reactivity patterns. The extra inner shells in potassium are shielded core electrons that do not participate in chemistry.

This is the deep reason the periodic table works: periodicity is a periodicity of valence configurations, not total electron count. Elements recur in the same column because every complete shell adds the same valence structure — one more s-electron beyond the core, etc. Quantum mechanics predicts that once you complete a shell and add one more electron to the next s-orbital, the chemical behavior resets to match the element one period above. The relevant physics (valence structure) has genuinely repeated, not just the row count.