Animated Solution for Chemistry - d and f-Block Elements: The pair that has similar atomic radii is

When we study the periodic table, one of the most fundamental rules we learn is that atomic radius increases as we move down a group. This makes perfect intuitive sense: as we go from one period to the next, a completely new principal quantum shell is added to the atom.

For the transition metals, this means we expect the elements of the $4d$ series to be significantly larger than those of the $3d$ series. And indeed, they are. Following this logic, we would naturally assume that the $5d$ series elements would be much larger than the $4d$ series elements. However, nature has a fascinating surprise waiting for us.

Lanthanoid Contraction

If we actually measure and plot the atomic radii of the $5d$ series, we find something astonishing. Instead of being much larger, the $5d$ elements are almost exactly the same size as the $4d$ elements located directly above them in the same group!

This unexpected overlap is caused by a phenomenon known as Lanthanoid Contraction. To understand why this happens, we have to look deep into the electronic configuration of these heavy atoms.

Before the $5d$ orbitals begin to fill with electrons, the atom must first fill the $4f$ orbitals. This means $14$ electrons are added to the $4f$ subshell.

Here is the critical catch: the shape of $f$-orbitals is highly complex and extremely diffused. Because they are so spread out, they are terrible at shielding the outermost electrons from the attractive pull of the positively charged nucleus. The order of shielding effect is strictly $s>p>d>f$.

Because these $14$ $4f$ electrons provide such poor shielding, the effective nuclear charge ($Z_{\text{eff}}$) experienced by the outermost electrons increases dramatically. The nucleus acts like an overpowered magnet, pulling the outer electron cloud much closer than we would normally expect. This inward contraction perfectly cancels out the increase in size that should have occurred from adding a new shell.

Because of Lanthanoid Contraction, elements in the $4d$ and $5d$ series belonging to the same group become almost identical in size.

Looking at our options, Molybdenum ($\text{Mo}$) is in the $4d$ series, and Tungsten ($\text{W}$) is right below it in the $5d$ series (Group 6). Their atomic radii are nearly identical ($r_{\text{Mo}}\approx r_{\text{W}}$).

This phenomenon creates pairs of elements known as chemical twins. Other famous examples include Zirconium and Hafnium ($\text{Zr}$ and $\text{Hf}$) in Group 4, and Niobium and Tantalum ($\text{Nb}$ and $\text{Ta}$) in Group 5. Because their sizes and valence electron configurations are so similar, their chemical properties are almost indistinguishable, making them notoriously difficult to separate in metallurgical processes!