Animated Solution for Chemistry - d and f-Block Elements: The atomic radius of Ag is closest to

When we look at the periodic table, one of the most fundamental rules we learn is that atomic size increases as we move down a group. This makes perfect intuitive sense: with each step down, a brand new principal quantum shell is added, placing the outermost electrons further away from the nucleus.

If we apply this logic to Group 11, we expect a clear progression. Copper (Cu) is in the $3d$ series, Silver (Ag) is below it in the $4d$ series, and Gold (Au) sits at the bottom in the $5d$ series. As expected, Silver is noticeably larger than Copper. But when we move from Silver to Gold, the universe throws a curveball. Instead of getting larger, Gold is almost exactly the same size as Silver! Both have an atomic radius of approximately $144\text{ pm}$. Why does this happen?

The Lanthanide Series

To understand this anomaly, we have to look at what happens in the periodic table before we reach Gold. Between the $4d$ series and the $5d$ series, a massive block of 14 elements is inserted. These are the Lanthanides (from $Z=58$ to $Z=71$).

As we move through the Lanthanide series, electrons are being added to the $4f$ orbitals. Here is the critical catch: $f$-orbitals have a highly diffused, complex shape. Because they are so spread out, $4f$ electrons are terrible at shielding the outermost electrons from the positive pull of the nucleus.

Because the $4f$ electrons provide such poor shielding, the effective nuclear charge ($Z_{\text{eff}}$) experienced by the outer electrons increases dramatically. The nucleus pulls the outer electron cloud inward with immense force.

This steady decrease in size across the $f$-block is called Lanthanide Contraction. By the time we finish filling the $4f$ orbitals and start filling the $5d$ orbitals (where Gold resides), the entire atom has shrunk significantly.

This contraction perfectly counteracts the expected increase in size that should have come from adding the new $n=6$ shell. The two opposing effects—the expansion from a new shell and the shrinkage from Lanthanide contraction—cancel each other out almost perfectly. As a result, the atomic radius of Gold ($5d$) is nearly identical to that of Silver ($4d$).

This is a high-yield concept for competitive exams: whenever you compare the sizes of $4d$ and $5d$ transition metals in the same group (like Zr and Hf, Nb and Ta, or Ag and Au), their radii will be remarkably similar due to Lanthanide contraction!