= Solution
The transport <mean free path> is $\ell=v_F\tau_{\rm tr}$, while $\mu=e\tau_{\rm tr}/m^*$. Eliminating the scattering time gives $\ell=\mu\hbar k_F/e$. The usual <ballistic focusing mobility criterion> $\ell\gtrsim L$ therefore gives
$$
\boxed{\mu_{\rm min}\sim\frac{eL}{\hbar k_F}=11.1\ \mathrm{m^2\,V^{-1}s^{-1}}
=1.11\times10^5\ \mathrm{cm^2\,V^{-1}s^{-1}}.}
$$
A more geometrically faithful first-peak survival criterion uses the semicircular path length $s=\pi L/2$, giving $\mu\gtrsim17.4\ \mathrm{m^2\,V^{-1}s^{-1}}$. There is no sharp universal visibility threshold: clearly resolved peaks favour $\ell\gg s$, small aperture broadening and <specular reflection>. The mobility inferred in part (ii) corresponds to $\ell\simeq314\ \mathrm{\mu m}$, comfortably above both estimates. Higher-order peaks can still be reduced by boundary roughness even when bulk mobility is high.
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