Suggest reasons why the $B-F$ bond lengths in $BF_{3}$ $(130 \ pm)$ and $BF_{4}^{-}$ $(143 \ pm)$ differ.

(N/A) The $B-F$ bond length in $BF_{3}$ is shorter than the $B-F$ bond length in $BF_{4}^{-}$.
$BF_{3}$ is an electron-deficient species. With a vacant $p$-orbital on boron, the fluorine and boron atoms undergo $p\pi-p\pi$ back-bonding to remove this deficiency. This imparts a partial double bond character to the $B-F$ bond.
This double-bond character causes the bond length to shorten in $BF_{3}$ $(130 \ pm)$.
However, when $BF_{3}$ coordinates with the fluoride ion, a change in hybridisation from $sp^{2}$ (in $BF_{3}$) to $sp^{3}$ (in $BF_{4}^{-}$) occurs.
Boron now forms $4 \sigma$ bonds and the double-bond character is lost. This accounts for a $B-F$ bond length of $143 \ pm$ in the $BF_{4}^{-}$ ion.