Suggest reasons why the B–F bond lengths in `BF_(3)` (130 pm) and `BF_(4 )^(– )`(143 pm) differ.

Explanation

In `BF_(3)`,B is `sp^(2)` hybridised and has only six electrons in the valence shell and behaves as an electron-deficient compound. To reduce its electron deficiency, `B` accept a pair of electron from filled `2p` orbital present on it. This is known as `ppi-ppi` back bonding which happens due to compatibility in the size and energy of `2p`orbital on `F` and `2p` orbital on `B` atom in `BF_(3)`.
Due to back-bonding in `BF_(3)` `B-F` bond acquires some double bond character resulting in shortening of the bond.
However, in `[BF_(4)](ө)`,B is `sp^(3)` hybridised and hence has eight electrons in its valence shell. Since there is an empty `p`-orbital available in `B` in `[BF_(4)](ө)` ion, back-bonding is not possible and `B-F` is purely single bond. Since double bonds are shorter than single bond, the `B-F` bond length in `BF_(3)` is shorter than in `[BF_(4)](ө)`.