Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 6, Problem 31E

(a)

To determine

To Compare:The tunneling probability when E is U01000 with that of when E is U0100 .

(b)

To determine

Whether the answer obtained supports the general rule that the transmission probability is very sensitive function of E .

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An electron with kinetic energy E = 3.10 eV is incident on a barrier of width L = 0.230 nm and height U = 10.0 eV (a) What is the probability that the electron tunnels through the barrier? (Use 9.11  10-31 kg for the mass of an electron, 1.055 ✕ 10−34 J · s for ℏ, and note that there are 1.60 ✕ 10−19 J per eV.)   b) What is the probability that the electron is reflected?   What If? For what value of U (in eV) would the probability of transmission be exactly 25.0% and 50.0%?   c) 25.0%   d) 50.0%
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Consider two identical conducting wires, lying on the x axis and separated by an air gap of thickness L=1nm. The work function of the metal is W=5 eV. (a) Find the probability that the electron will emerge on the other side of the barrier? (b) Find the electric field needed to allow the tunneling probability of 10-5.
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