  We study the Hilbert expansion for small Knudsen number $\varepsilon$ for the
Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term
takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi
\theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\
}\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).$ Our main result states that if the
Hilbert expansion is valid at $t=0$ for well-prepared small initial data with
irrotational velocity $u_0$, then it is valid for $0\leq t\leq \varepsilon
^{-{1/2}\frac{2k-3}{2k-2}},$ where $\rho_{0}(t,x)$ and $ u_{0}(t,x)$ satisfy
the Euler-Poisson system for monatomic gas $\gamma=5/3$.
