Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section F / 46 / a / iv / B / Solution

Let ${\kappa }_0=\sqrt{2m{V}_0}/\hslash$. As $E\to 0^{+}$, $\kappa \to {\kappa }_0$ while the large denominator term scales as $1/E$. HenceThe limit is linear in incident energy for fixed positive height and nonzero width. A below-barrier wave has nonzero penetration at finite energy, but that does not imply a finite zero-energy transmitted flux.