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Tunneling Probability of an Electron with Given Kinetic Energy in a Square Well

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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 calculate the tunneling probability of an electron with given kinetic energy across a barrier of given energy 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

-hbar^2/2m psi''(x) + V0 psi(x) = E psi(x),

where m = 9.11 * 10^-31 kg is the mass of the electron, E is its ...

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