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Chapter 37: Problem 10

A particle of energy \(E=5 \mathrm{eV}\) approaches an energy barrier of height \(U=8 \mathrm{eV}\). Quantum mechanically there is a finite probability that the particle tunnels through the barrier. If the barrier height is slowly decreased, the probability that the particle will reflect from the barrier will a) decrease. b) increase. c) not change.

Short Answer

Expert verified
Answer: The probability that the particle will reflect from the barrier will decrease.

Step by step solution

01

Remember the relationship between transmission and reflection probabilities

In quantum mechanics, a particle can either be reflected or transmitted (tunnel) when it encounters a barrier. Their probabilities should add up to 1, i.e. \(P_{reflection} + P_{transmission} = 1\).
02

Compare the initial energy and barrier height

The particle has an energy E = 5 eV, and it encounters an energy barrier with a height of U = 8 eV. Since the particle energy is less than the barrier height, there's a higher chance of reflection and a smaller chance of transmission (tunneling).
03

Visualize the decrease in barrier height

As the barrier height is reduced from 8 eV to a smaller value, the particle has a higher probability of tunneling through the barrier, as its energy can overcome the barrier's height more easily.
04

Determine the effect on reflection probability

Since the transmission probability increases with the decrease in barrier height, the reflection probability should decrease accordingly. This is because the sum of reflection and transmission probabilities should be equal to 1. So, the answer is: a) The probability that the particle will reflect from the barrier will decrease.

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