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 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 hybridization 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.