AP Chemistry · Lesson 3

Periodic trends and Coulomb's law

Know Know it

Every periodic trend comes back to Coulomb's law: the attraction between the nucleus and an electron grows with the charges and falls with distance, F∝q1q2r2F \propto \frac{q_1 q_2}{r^2}.

Across a period, protons are added but the electrons go into the same shell, and core electrons stay the same. The effective nuclear charge rises, so atoms get smaller, ionization energy rises and electronegativity rises.

Down a group, each new period adds a shell. The outer electrons are farther away and shielded by more core electrons, so atoms get larger and ionization energy falls, even though the nucleus has more protons.

Ions: a cation is smaller than its atom, and an anion is larger. For ions with the same number of electrons, the one with more protons is smaller.

Successive ionization energies rise slowly while valence electrons are removed, then jump sharply when the next electron must come from a core shell. The jump tells you how many valence electrons the atom has.

Which of these atoms has the largest atomic radius?

  1. Sodium
  2. Chlorine
  3. PotassiumAnswer
  4. Bromine

How to solve it

  1. Size grows down a group (more shells) and shrinks across a period (more protons in the same shell).
  2. The largest atom is the one lowest and farthest left: potassium, in period 4, group 1.

Why each choice is right or wrong

  • A. Incorrect. Sodium is in group 1 too, but its valence electron is in the third shell, one shell closer than potassium's.
  • B. Incorrect. Chlorine is at the right of period 3; its high effective nuclear charge pulls its electrons in, making it small.
  • C. Correct. Potassium is at the left of period 4: its valence electron is in the fourth shell and feels a low effective nuclear charge.
  • D. Incorrect. Bromine is in period 4 like potassium, but its many more protons in the same shell pull its electrons closer.

Trap Two dips in the ionization energy trend

Ionization energy rises across a period, but not every step. Aluminum is lower than magnesium because its electron comes from 3p, which is higher in energy than 3s. Sulfur is lower than phosphorus because its fourth 3p electron shares an orbital with another electron, and their repulsion makes it easier to remove.

Explain Explain it

Task verbs: explain, compare

A full particle-level explanation names both atoms, compares them on the two variables in Coulomb's law (the charge the electron feels and its distance from the nucleus) and then ties that to the property. For example, for two atoms in one period: same shell, so similar distance and the same core shielding; more protons, so a stronger pull; so the electron is harder to remove.

"It wants a full octet" or "it is more stable" is not an explanation. Say what attracts what, and why it is stronger or weaker.

Successive ionization energies of an element in period 3 (kJ/mol)

FirstSecondThirdFourth
5781817274511 577

Which element is it?

  1. Magnesium
  2. AluminumAnswer
  3. Silicon
  4. Sodium

How to solve it

  1. Look for the largest jump: 2745 to 11 577 kJ/mol, between the third and fourth.
  2. Three electrons come off before a core electron is reached, so there are 3 valence electrons.
  3. The period 3 element with 3 valence electrons is aluminum, [Ne] 3s² 3p¹.

Why each choice is right or wrong

  • A. Incorrect. Magnesium has 2 valence electrons, so its big jump would come between the second and third ionization energies.
  • B. Correct. The jump comes after the third electron (2745 to 11 577 kJ/mol), so the atom has 3 valence electrons: aluminum, in group 13.
  • C. Incorrect. Silicon has 4 valence electrons, so its fourth ionization energy would still be a valence electron with no huge jump.
  • D. Incorrect. Sodium has 1 valence electron, so its big jump would come right after the first ionization energy.

Explain why a chloride ion, Cl⁻, is larger than a neutral chlorine atom. In your answer, compare the number of protons and the number of electrons in the two particles.

Compare with a model answer

A full answer does this

  • States that both particles have the same number of protons, 17
  • Explains that the ion has one more electron (18 versus 17), which adds repulsion among the electrons or lowers the pull per electron, so the electron cloud spreads out

Model answer

The chlorine atom and the chloride ion both have 17 protons, so the nuclear charge is the same. The ion has 18 electrons instead of 17. The extra electron adds repulsion among the valence electrons, and the same 17 protons now pull on more electrons, so the electron cloud spreads out and the ion is larger than the atom.

Apply Apply it

Practice these topics. AP Practice questions on exactly what this lesson covers, with an explanation for every answer.