How Deep Should a Finite Square Well Be for Two Electron Energy Levels?

In summary, to find the necessary depth of the finite square well, you can use equations (1) and (2) to iteratively adjust the potential depth Vo until the quantum number u takes on a value of 1 or 2.
  • #1
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Homework Statement



A finite square well 2.0fm wide contains one electron. How deep must the well be if there are only two allowed (bound) energy levels for the electron?

Homework Equations



(1) E = [ a^2 * hbar^2 ] / 2m
(2) u = sqrt [2m(E+Vo)] / hbar

The Attempt at a Solution



Use equation (1) to find E, a is the width
Then use the E to find u in equation. Vo = 0 because it's in the box

On the right track? Or completely off?
 
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  • #2
Yes, you are on the right track. To solve this problem, you can use equations (1) and (2). Since there are only two allowed energy levels for the electron, equation (1) can be rearranged to find the potential depth Vo given the energy E: Vo = 2mE/a^2 - hbar^2/2m Then, equation (2) can be used to find the quantum number u with the potential depth Vo: u = sqrt[2m(E+Vo)] / hbar Since there are only two allowed energy levels, the quantum number u must have a value of either 1 or 2. Therefore, you can iteratively adjust the potential depth Vo until the quantum number u takes on one of these values.
 

Related to How Deep Should a Finite Square Well Be for Two Electron Energy Levels?

1. What is the depth of a finite square well?

The depth of a finite square well is the difference between the maximum potential energy and the minimum potential energy within the well. It is typically measured in units of energy, such as electron volts (eV) or joules (J).

2. How is the depth of a finite square well determined?

The depth of a finite square well is determined by the depth of the potential barrier that forms the boundaries of the well. This potential barrier can be adjusted by changing the material and dimensions of the well, such as its width and height.

3. What is the significance of the depth of a finite square well?

The depth of a finite square well affects the behavior of particles within the well. A deeper well will have a higher probability of trapping particles, while a shallower well will allow particles to escape more easily. This can have implications in various fields of physics, such as in quantum mechanics and solid state physics.

4. How does the depth of a finite square well impact energy levels?

The energy levels of particles within a finite square well are determined by the depth of the well. A deeper well will have a larger number of discrete energy levels, while a shallower well will have fewer energy levels. The depth of the well also affects the spacing between energy levels.

5. Can the depth of a finite square well be changed?

Yes, the depth of a finite square well can be changed by adjusting the potential barrier that forms its boundaries. This can be done by altering the material or dimensions of the well. Additionally, the depth of the well can also be changed by applying an external force or potential to the system.

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