Answer
$m(Br_2)=1.422g$
Work Step by Step
The following reaction takes place:
$Cl_2+2KBr\rightarrow Br_2 + 2KCl$
Considering stoichiometric coefficients, we can conclude that
$m(Br_2)=m(Cl_2)\times \frac{M(Br_2)}{M(Cl_2)}=0.631g \times \frac{160\frac{g}{mol}}{71\frac{g}{mol}}=1.422g$