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Percentage of Electrons Tunneling Through?

  1. Nov 9, 2015 #1
    1. The problem statement, all variables and given/known data

    A stream of electrons is of energy E is incident on a potential barrier of height U and thickness d. Even though U >> E, 5% of the electrons tunnel through the barrier. If the thickness of the barrier decrease to 0.86 d, what percentage of the electrons will tunnel through?


    2. Relevant equations

    P(d) = 0.05 = exp(-2αd)
    P(d*a) = exp(-2αd*a) = exp(-2αd)^a = 0.05^a

    Here a is a constant.

    Convert to %.


    3. The attempt at a solution

    At first I tried "reasoning" my way through it (haha), thinking that if the thickness (d) decreased from an arbitrary 1 (100%) to a 0.4 (40%), then that's a 60% change in the thickness, meaning the 5% would also change by 60%, making that a 3%.

    But clearly...I'm missing something right in front of me. I guess what's throwing me this time is the equation offered in the hint of: P(d*a) = exp(-2αd*a) = exp(-2αd)^a = 0.05^a. Where did the "a" come from, and where do plug in numbers to convert it to said percent?
     
  2. jcsd
  3. Nov 9, 2015 #2

    haruspex

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    The hint is true for any a. You need to choose a value for a which is relevant to the problem.
     
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