Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 40, Problem 21P

(a)

To determine

The transmission coefficient.

(b)

To determine

The width of the barrier to increase the transmission coefficient by one in one million.

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An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown in Figure P40.21. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero.(b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrierto be one in one million?
The table gives relative values for three situations for the barrier tunneling experiment of the figures. Electron Energy Barrier Height Barrier Thickness (a) 5E L (b) 17E L/2 (c) 2E 2L Energy V-0 V<0 V-0 Electron * 0 x l. Rank the situations according to the probability of the electron tunneling through the barrier. If multiple situations rank equally, use the same rank for each, then exclude the intermediate ranking (i.e. if objects A, B, and C must be ranked, and A and B must both be ranked first, the rạnking would be A:Greatest, B:Greatest, C:Third greatest). If all situations rank equally, rank each as 'Greatest'. (a) (b) (c)
= = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nm
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