The element that does not show catenation is

First, let us recall the meaning of the term “catenation”. Catenation is the self-linking property of an element through covalent bonds, resulting in chains or rings of identical atoms. Its extent depends mainly on the strength (bond enthalpy) of the element-element single bond. The higher the $$E\_{X-X}$$ bond enthalpy, the greater is the tendency toward catenation.

Now, we focus on the elements given in the options. All of them—$$\text{Si},\; \text{Ge},\; \text{Sn},\; \text{Pb}$$—belong to group $$14$$ of the periodic table, lying below carbon. Down a group, the atomic size increases and the $$X\!-\!X$$ bond enthalpy decreases. Mathematically, we can summarise the trend:

$$E_{\text{C-C}} \; > \; E_{\text{Si-Si}} \; > \; E_{\text{Ge-Ge}} \; > \; E_{\text{Sn-Sn}} \; > \; E_{\text{Pb-Pb}}$$

The loss in bond strength arises because larger, more diffused orbitals overlap less efficiently, making the bond weaker and longer. As a consequence, the ability of the atoms to form stable chains falls sharply down the group.

Let us compare the approximate single-bond enthalpies (kJ mol−1) for clarity:

$$\begin{aligned} E_{\text{Si-Si}} &\approx 226,\\ E_{\text{Ge-Ge}} &\approx 188,\\ E_{\text{Sn-Sn}} &\approx 155,\\ E_{\text{Pb-Pb}} &\approx 110. \end{aligned}$$

Because the $$\text{Pb-Pb}$$ bond is the weakest among these, two adjoining lead atoms cannot sustain a long chain. Therefore $$\text{Pb}$$ hardly exhibits catenation in ordinary chemical conditions. In contrast, silicon, germanium and even tin still possess sufficiently strong $$X\!-\!X$$ bonds to show at least limited catenation: polysilanes ($$\text{Si}_n\text{H}_{2n+2}$$-type), polygermanes and stannanes ($$\text{Sn}_n\text{H}_{2n+2}$$-type) are all known.

Hence, among the given choices, lead is the element that does not show catenation.

Hence, the correct answer is Option D.