k2 = root 2m (V0 ?E)/h The scanning tunneling electron microscope takes advantag

Question

k2 = root 2m (V0 ?E)/h The scanning tunneling electron microscope takes advantage of the ability of electrons to tunnel across barriers too high to surmount art thereby allows the topography of surfaces to be mapped on an atomic scale. Protons also take advantage of the tunnel effect during rapid proton transfer in solution, and therefore contribute to the properties of acids and bases. The probability of transmission through a potential barrier is given by T = [ 1 + V^2 0(e^k2l ? e^-k2L)^2/16E(V0 ? E)^-1 where E is the incident energy, V0 and L are the barrier's height and width respectively and k2 as given above. Calculate the probability that an electron with a kinetic energy of 3eV will tunnel through the barrier if it is 65 pm thick and the potential barrier is 5eV high. (Careful with your units!)

Explanation / Answer

k2 = 1.151*10^9 1/m

Substituiting the values, T = 0.994

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