Why the bond dissociation enthalpy of `F_2` is less than that of `Cl_2`.

Explanation

B and F atoms are elements of the samme period (second period), having comparable sizes. In `BF_(3)`, the octet of B-atom is not filled up. To fullfill the octet, B-atom participates in the resonance (`pi`-back bonding) with the f-atoms. This resonance involving orbitals of comparable sizes (2p-2p overlap) is very effective. as a result, electron density on B-atom increases, and tendencyy of `BF_(3)` to behave as a lewis acid decreases. on the other hand, Br is an element of fourth period. in `B Br_(3)`, effective `pi`-back bonding involving orbitals of dissimilar sizes (2p-4p overlap) does not take place. hence, the electron density on B does not increase and therefore, `B Br_(3)` behaves as a stronger Lewis acid than `BF_(3)`.