The graph below represents the ground state wave function of an electron in a fi

Question

The graph below represents the ground state wave function of an electron in a finite square well potential of width L. The potential is zero at x = 0.


a) Where are the boundaries of the potential well?

The left boundary is at x = _____ picometers,

and the right boundary is at x = ______picometers.

b) The wave function of the electron within the well is of the form A cos( 2px / ? ) where A is a normalization constant.

What is the approximate value of ?, within about 10%?

? = ________ picometers.

c) What is the approximate kinetic energy of the electron inside the well?

Kinetic energy = ____________ eV.

d) Now consider an infinite square well potential of the same width L. When the electron is in the ground state of this infinite well, is its kinetic energy higher (answer 1) or lower (answer 2) than its kinetic energy in the ground state of the finite well?

The kinetic energy would be _____________

e) If the electron were in the ground state of an infinite square well of the same width L, what would be its kinetic energy?

Its kinetic energy = ____________eV.

Explanation / Answer

For the portion d) The wavelength in the sinusoidal part of each wave would be larger in finite well. This larger wavelength results in lower momentum by p=h/lamda. If the momentum drops, so does the KE respectively since the mass of an electron is constant.

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