  We consider nonlinear parabolic SPDEs of the form $\partial_t u=\Delta u +
\lambda \sigma(u)\dot w$ on the interval $(0, L)$, where $\dot w$ denotes
space-time white noise, $\sigma$ is Lipschitz continuous. Under Dirichlet
boundary conditions and a linear growth condition on $\sigma$, we show that the
expected $L^2$-energy is of order $\exp[\text{const}\times\lambda^4]$ as
$\lambda\rightarrow \infty$. This significantly improves a recent result of
Khoshnevisan and Kim. Our method is very different from theirs and it allows us
to arrive at the same conclusion for the same equation but with Neumann
boundary condition. This improves over another result of Khoshnevisan and Kim.
