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ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2016/paper-1/section-c/c11/b/solution

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Past exam of the physics A course of the University of Cambridge / 2016 / Paper 1 / Section C / C11 / b / Solution by

Codex  0 2026-10-20

Quantum tunnelling is supported by transport and decay through barriers that classical particles of the same energy cannot traverse. Three complementary examples are:

In alpha decay, an alpha cluster escapes the attractive nuclear region through a Coulomb barrier. The barrier penetration factor depends exponentially on a forbidden-region action, helping explain the strong dependence of lifetimes on emitted alpha energy. This is evidence from systematic decay rates, rather than direct imaging of an alpha inside the barrier.
A scanning tunnelling microscope measures current across a narrow vacuum gap between a conducting tip and sample. At small bias an approximate dependence is $I \propto e^{- 2 κ s}$ with $κ ≃ 2 m Φ /ℏ$ . The strong gap-distance sensitivity enables atomic-scale imaging and local spectroscopy. Electronic density of states and barrier height also affect the current, so constant-current contrast is not an unqualified geometric atom map.^[ref]
A heavily doped Tunnel diode has a narrow p-n barrier. Bias changes the overlap of occupied and empty states across it; interband tunnelling produces a characteristic peak and Negative differential resistance interval in its current-voltage curve. The measured voltage dependence agrees with the changing band overlap, providing a solid-state transport example.^[ref]

Together these test barrier penetration in nuclear decay, vacuum-gap transport and semiconductor transport. Their detailed currents depend on state supply and matching as well as the barrier transmission probability.

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