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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).

    I need the step-by-step solution please.

    Thank You.

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    Solution Preview

    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 ...

    Solution Summary

    We calculate the tunneling probability of an electron with given kinetic energy across a barrier of given energy and thickness.