What is lanthanoid contraction?

What happens inside the lanthanide atoms?

1. Electronic Configuration
   Each lanthanide element adds one extra proton in the nucleus and one extra electron mainly into the 4f subshell:
   $[Xe] \, 4f^{1-14}\, 5d^{0-1}\, 6s^2$

2. Poor Shielding by 4f Electrons
   • Electrons in the f-orbitals are diffused and lie deep inside the atom.
   • They do not shield (block) the increasing positive nuclear charge effectively.

3. Effective Nuclear Charge ($Z_{\text{eff}}$)
   Because shielding is poor, the outer 5d and 6s electrons feel a stronger pull from the nucleus as we move from La ($Z = 57$) to Lu ($Z = 71$).

4. Result
   Radii of $\text{Ln}^{3+}$ ions decrease almost smoothly and steadily along the series:
   $r_{\text{La}^{3+}} \approx 1.06\,\text{Å},\; r_{\text{Lu}^{3+}} \approx 0.85\,\text{Å}$

This gradual decrease in ionic and atomic radii across the lanthanides is called lanthanoid contraction.

Why students should care

• Explains very close sizes of 2nd & 3rd transition series elements (Zr–Hf, Nb–Ta, etc.).
• Affects hardness, density, and separation chemistry of lanthanides.

Imagine a Line of 4th-Standard Students!

Suppose 14 students (named La, Ce, Pr … Lu) stand in a line, and every new student must hold a heavy invisible school bag (called 4f electrons).
Because of that bag, each new student cannot spread arms widely; he gets pulled a little bit closer to the teacher.
So as new students join, their distance from the teacher keeps shrinking little by little even though they all have almost the same height.

That steady shrinking of size from the first student (La) to the last (Lu) is what chemists call “lanthanoid contraction”.

Definition & Key Points

1. Definition
   Lanthanoid contraction is the steady decrease in the atomic and ionic radii of the trivalent lanthanide ions ($Ln^{3+}$) from $La$ to $Lu$ as atomic number increases.

2. Cause
   $\text{Poor shielding by 4f electrons} \; \longrightarrow \; \text{higher } Z_{\text{eff}} \; \longrightarrow \; \text{electrons pulled inward}$

3. Quantitative Trend
   $r_{La^{3+}} > r_{Ce^{3+}} > \dots > r_{Lu^{3+}}$

4. Consequences
   • Almost identical sizes of 4d & 5d transition metals (Zr–Hf).
   • Increased density & hardness of later lanthanides.
   • Difficulty in separation of lanthanide ions because size difference is small.

Thus, lanthanoid contraction = continuous decrease in size across lanthanide series due to inadequate shielding of nuclear charge by 4f electrons.