  In this paper we investigate blocks of symmetric groups of weight 2 over
fields of odd characteristic $p$. We develop an algorithm that relates the
quivers of two such blocks forming a $(2:1)$ pair, as introduced by Scopes. We
then apply the algorithm to blocks whose $p$-cores are hook partitions, in
order to explicitly determine the quivers of these blocks. As a consequence we
conclude that two $p$-blocks $B_1$ and $B_2$ of symmetric groups of weight $2$
whose $p$-cores are hook partitions are Morita equivalent if and only if $B_2$
or its conjugate block is in the same Scopes class as $B_1$.
