ARCH-process with exponencial variance function

[Mst]

I need some help for a proof regarding Engles ARCH-paper from 1982.

For an ARCH-process with a variance function
h_t = exp(a_0 + a_1 y_{t-1}^2)
he states, that the data generatet from this model has infinite variance (or goes to infinity) whenever a_1 is not zero.

I need to explain why or even proof that, can you give me some help/ideas?

Thanks!