What is quantum tunneling? Calculate (i) the tunneling length and (ii) the tunneling probability when an electron of energy 4.0 eV is incident on a potential barrier of height 10 eV and width of 0.2 nm.
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Expert's answer
2021-11-01T19:25:13-0400
Quantum tunnelling is the quantum mechanical phenomenon where a particle (more accurately, its wavefunction) can propagate through a potential barrier.
Let tunneling lenght be a=0.2nm=0.2×10−9m, the energy of the particle E=4eV≈6.409×10−19J and the potential height U=10eV≈16.02×10−19J. The tunneling propability is then given as follows (see https://courses.physics.illinois.edu/phys485/fa2015/web/tunneling.pdf, page 13):
T=(1+4(E/V)(1−E/V)sinh2(βa))−1
where β=ℏ2m(V−E), m=9.1×10−31kg is the mass of electron and ℏ=1.055×10−34Js. Thus, obtain:
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