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Chapter 40: Q. 9 (page 1174)

An electron has a 0.0100 probability (a 1.00% chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be0.0050,0.0025or0.0001? Explain.

Short Answer

Expert verified

The width of the barrier is doubled , will the tunneling probability be0.0050,0.0025or0.0001isPtunnel,2=0.0001.

Step by step solution

01

Given Information

We have to given that an electron has a 0.0100, the width of the barrier is doubled, will the tunneling probability be 0.0050,0.0025or0.0001.

02

Simplify

Ptunnel,2=The probability that the electron is the tunnel through the barrier is given as the equation:

Ptunnel=e-2蝇畏

and we are given that the initial probability is 0.01, so let the probability after the width of the barrier is doubled be Ptunnel,2since:

蝇1is the initial width after doubling. Notice that eab=eab. Then:

role="math" localid="1650132194389" Ptunnel,2=exp-4蝇1畏=exp-2蝇1畏2=Ptunnel,12Ptunnel,2=0.0001

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