Questions: Electron Configuration and the Aufbau Principle

Question 1

Potassium has 19 electrons. After filling through 3p, where does the 19th electron go, and why?

• A. Into 3d, because 3d has a lower principal quantum number (n=3) than 4s (n=4)
• B. Into 4s, because the (n+ℓ) rule gives 4s a value of 4 while 3d has a value of 5, so 4s has lower energy
• C. Into 4p, because electrons always complete one subshell type before starting the next
• D. Into 3d, because d orbitals fill before s orbitals in the same period of the periodic table

Answer: (B)

The 19th electron goes into 4s, not 3d. For 4s: n+ℓ = 4+0 = 4. For 3d: n+ℓ = 3+2 = 5. Lower (n+ℓ) fills first, so 4s fills before 3d. The common misconception is to fill by n alone, which would incorrectly place 3d (n=3) before 4s (n=4). In multi-electron atoms, effective nuclear charge and shielding split subshell energies in a way that makes this crossing necessary.

Question 2

Why do sodium (Na) and potassium (K), which are in the same column of the periodic table, show similar chemical behavior?

• A. They have the same total number of electrons in their atoms
• B. They have the same number of neutrons in their nuclei
• C. They have the same valence electron configuration — both have a single electron in an outermost s subshell ([noble gas] ns¹)
• D. They have similar atomic masses, so they behave similarly in chemical reactions

Answer: (C)

Chemical behavior is determined by valence electrons — the outermost electrons that participate in bonding. Na is [Ne]3s¹ and K is [Ar]4s¹; both have one electron in an outermost s orbital. This identical valence configuration produces similar reactivity (both readily lose one electron to form +1 ions). Column placement in the periodic table directly encodes valence electron configuration, which is why periodic trends are possible.

Question 3

In multi-electron atoms, the 4s subshell fills before 3d because electrons in 4s experience greater effective nuclear charge and lower energy than those in 3d.

• T. True
• F. False

Answer: True

In hydrogen, all subshells with the same n are degenerate. In multi-electron atoms, inner electrons shield outer electrons from the nucleus, and different subshells penetrate the electron cloud differently. The 4s orbital penetrates closer to the nucleus on average than 3d, giving it lower energy despite the higher principal quantum number. The (n+ℓ) rule is a practical summary of this effect.

Question 4

In multi-electron atoms, as in hydrogen, most subshells with the same principal quantum number n have the same energy (are degenerate).

• T. True
• F. False

Answer: False

Degeneracy of same-n subshells holds only for hydrogen (a one-electron atom with no electron-electron repulsion). In multi-electron atoms, electron-electron repulsion and differential shielding break the degeneracy: 2s and 2p have different energies, as do 3s, 3p, and 3d. This is precisely why 4s fills before 3d — the orbital energies depend on both n and ℓ in multi-electron atoms.

Question 5

Explain why 4s fills before 3d in multi-electron atoms, even though 3 is a smaller principal quantum number than 4.

Model answer: In multi-electron atoms, orbital energy depends on both n and ℓ, not n alone. Inner electrons shield outer electrons from the nucleus. The 4s orbital penetrates closer to the nucleus than 3d (despite higher n), giving it lower energy in multi-electron atoms. The (n+ℓ) rule captures this: 4s has n+ℓ = 4, while 3d has n+ℓ = 5, so 4s has lower energy and fills first.

This is one of the most important departures from the naive 'fill by n' picture. In hydrogen, subshells with the same n are degenerate. But electron-electron repulsion in multi-electron atoms creates an energy splitting that depends on the orbital's shape (ℓ) as well as its size (n). The crossing of 4s below 3d is the reason the transition metals (d-block) appear where they do in the periodic table, and it directly explains why period 4 starts with K and Ca (filling 4s) before Sc–Zn (filling 3d).