= Solution
Confinement to <length> $L$ gives a <momentum> scale $p\sim\hbar/L$ by the <Heisenberg uncertainty principle>. Using the alpha-particle <mass> $m_\alpha\simeq6.64\times10^{-27}\,\mathrm{kg}$, its speed scale is $v\sim\hbar/(m_\alpha L)$. Counting encounters with either wall,
$$
\boxed{\nu\sim\frac vL\sim\frac{\hbar}{m_\alpha L^2}
\simeq1.6\times10^{20}\,\mathrm{s^{-1}}.}
$$
This is an order-of-magnitude collision-rate estimate, not a classical trajectory of a stationary <quantum state>. Taking $\Delta x\Delta p=\hbar/2$, a different geometric interpretation of the well size, or successive returns to the same wall changes the coefficient by factors of order unity; the robust scale is $10^{20}\,\mathrm{s^{-1}}$.
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