Past exam of the physics A course of the University of Cambridge / 2021 / Paper 1 / Section A / 2 / Solution

Inside the rectangular potential barrier, the electron's wavefunction is evanescent, with decay constantFor width $a=1\mathrm{nm}$, the squared exponential suppression in the quantum tunnelling probability isThis is the usual leading-exponential estimate. The rectangular-barrier tunnelling probability, retaining the interface-matching prefactor for equal potentials on the two sides, isHere that prefactor is $16(8)(2)/10^2=2.56$, so the more accurate result is $\boxed{T\simeq 1.30\times 10^{-6}}$. Both estimates show that transmission is of order one part in a million. A classical particle with this kinetic energy cannot cross the barrier at all.