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Problem in Quantum Mechanical Tunneling

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Given a tunneling barrier with a thickness of 2nm and a barrier height of 5eV, what is the minimum kinetic energy an electron would have to have to have a 50% chance of passing through? (hint it doesn't necessarily have to be less than the barrier height)

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Solution Summary

We compute the kinetic energy an electron must have in order to have a 50% probability of tunneling through a barrier of given height and thickness.

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To calculate the tunneling probability, we first need to solve the Schrodinger equation for the wavefunction of the electron inside the barrier. We have
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