  Let $\mb w$ be a morphic word over a finite alphabet $\Sigma$, and let
$\Delta$ be a nonempty subset of $\Sigma$. We study the behavior of maximal
blocks consisting only of letters from $\Delta$ in $\mb w$, and prove the
following: let $(i_k,j_k)$ denote the starting and ending positions,
respectively, of the $k$'th maximal $\Delta$-block in $\mb w$. Then
$\limsup_{k\to\infty} (j_k/i_k)$ is algebraic if $\mb w$ is morphic, and
rational if $\mb w$ is automatic. As a result, we show that the same conclusion
holds if $(i_k,j_k)$ are the starting and ending positions of the $k$'th
maximal zero block, and, more generally, of the $k$'th maximal $x$-block, where
$x$ is an arbitrary word. This enables us to draw conclusions about the
irrationality exponent of automatic and morphic numbers. In particular, we show
that the irrationality exponent of automatic (resp., morphic) numbers belonging
to a certain class that we define is rational (resp., algebraic).
