The reason chlorine (Cl) cannot undergo sp3 hybridization in the context of BCl3 is related to the electronic configuration and valence shell structure of chlorine.
Chlorine, as a halogen, has an atomic number of 17, meaning it has 17 electrons. Its electronic configuration is 1s2 2s2 2p6 3s2 3p5, with three electrons in its valence shell (3s and 3p orbitals).
To form three covalent bonds with boron in BCl3, each chlorine atom needs to contribute one electron from its valence shell. Since chlorine already has three electrons in its 3p orbital, it would require the promotion of an electron from the 3s orbital to the 3p orbital to allow for sp3 hybridization.
However, the energy required for this electron promotion is relatively high, and it is not energetically favorable for chlorine to undergo sp3 hybridization in this scenario. Instead, chlorine prefers to use its three 3p orbitals for bonding, which results in the formation of three sigma (σ) bonds with boron through linear overlap between the empty p orbital of chlorine and the hybridized orbitals of boron.
Therefore, in BCl3, the boron atom undergoes sp2 hybridization to form three sigma bonds, while chlorine does not undergo sp3 hybridization but utilizes its 3p orbitals for bonding.