An electron with energy E is incident upon a potential energy barrier of height E_pot E and thickness L.The transmission coefficient T: A)is zero B)decreases exponentially with L C)is proportional to 1/L D)is proportional to 1/L² E)is non-zero and independent of L

Question

An electron with energy E is incident upon a potential energy barrier of height E_pot > E and thickness L.The transmission coefficient T: A)is zero B)decreases exponentially with L C)is proportional to 1/L D)is proportional to 1/L² E)is non-zero and independent of L

Quizplus · Accepted Answer

The transmission coefficient T decreases exponentially with L according to the exponential decay law: T = e^(-2κL), where κ = sqrt(2m(E_pot - E))/ħ is the wave vector inside the potential barrier. As L increases, κ increases and T decreases rapidly. Therefore, choice B is the best answer. Choices A, C, and D are incorrect because they imply either zero transmission, inverse proportionality to L, or inverse proportionality to L^2, which are not consistent with the physical behavior of electron tunneling through a potential barrier. Choice E is incorrect because it implies a constant transmission, which is not true in general.

An Electron with Energy E Is Incident Upon a Potential