Question

explain why bf3 exits whereas bh3 does not ?

Answer 1

Actually BH3 does exist. It is a very common reagent used in the hydroboration of double boonds, and in the reduction of amides to amines. After adding across double bonds the borane can be hydrolysed to the alcohol, effectively completing the addition of water across a double bond. Improtantly this addition is completed in an anti-Markovnikov manner, because in BH3 the H are electronegative, whereas in water they are electropositive. 

Because of its instability it exists as a dimer, B2H6, where elextrons are shared between each of the monomers. It is a gas, but is used in chemistry as solutions in THF, pyridine or dimethyl sulfide. In these solutions the lone pair of electrons from the oxyge,, nitrogen or sulfur, are donated to the empty p orbital of boron, stabilising the BH3:solvent complex. 

Borane chemistry is a massive field and has enormous use in synthetic organic chemistry, with BH3 being exceptionally useful for a number of transformations and funcional group interconversions.