Calculating Quantum Tunneling Probability - 1.524 eV, 343 pm, 2.654 eV

AI Thread Summary
The discussion centers on calculating the transmission probability of an electron with an energy of 1.524 eV through a barrier of 343 pm and a potential height of 2.654 eV. It emphasizes that the potential energy before and after the barrier is not crucial as long as it remains below 1.524 eV, allowing for a traveling wave. The user has successfully calculated the decay constant, kappa, using the formula K = √{[2m(E-V0)] / (h-bar^2)}. The final transmission probability can be determined using the expression exp(-2 * kappa * barrier thickness). This approach highlights the importance of barrier thickness in quantum tunneling calculations.
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Homework Statement


What is the approximate transmission probability (in %) of an electron with total energy 1.524 eV through a barrier of thickness 343 pm, and a potential height of 2.654 eV? (Does it matter what the potential energy is before and after the barrier? Not really, as long as it is <1.524 eV, so in both cases there is a traveling wave.)

Homework Equations


None given however I believe it has something to do with: http://en.wikipedia.org/wiki/Transmission_coefficient

I've managed the previous question which was about probability of transmission however it didn't deal with barrier thickness which I am not accustomed to. I can't find any literature on the subject other than the Wikipedia article I linked.

The Attempt at a Solution


No real attempt, I managed to calculate Kappa which is
K = Square root of {[2m(E-V0)] / (h-bar^2)}
 
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Figured it out! It's exp(-2 *kappa *barrier thickness)
 

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