  We consider the critical alternating quantum spin chain with ${q_{+}\over
2}$, ${q_{-} \over2}$ spins. Using the Bethe ansatz technique we find explicit
expressions for the $S$-matrix of the model. We show that in the limit that
$q_{\pm} \rightarrow \infty$ our results coincide with the ones obtained for
the principal chiral model level one, for the LL (RR) LR scattering. We also
study the scattering of the bound states of the model and we recover the
results of the XXZ (sine -Gordon) model.
