Electron confined in a one dimensional box

In summary, the conversation discusses an electron confined in a one-dimensional box and its observed energies of 27 eV, 48 eV, and 75 eV at different times. The question asks for the length of the box, with a hint to assume that the quantum numbers of these energy levels are less than 10. The suggested equation for solving for length is E=h^2n^2/(8mL^2), where energy is proportional to n^2/L^2. With energies given for three states, the length can be determined.
  • #1
tboyers
5
0

Homework Statement


An electron confined in a one-dimensional box is observed, at different times, to have energies of 27 eV , 48 eV , and 75 eV .
What is the length of the box? Hint: Assume that the quantum numbers of these energy levels are less than 10.

Homework Equations



E=h^2n^2/(8mL^2)

The Attempt at a Solution


I tried using that equation to solve for length, but I don't know what energy levels these are at, so i can't seem to solve it.
 
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  • #2
tboyers said:
I tried using that equation to solve for length, but I don't know what energy levels these are at, so i can't seem to solve it.
energy of the states are proportional to n^2/L^2 and you have energies for three states so can you find out L?
 

FAQ: Electron confined in a one dimensional box

1. What is an electron confined in a one dimensional box?

An electron confined in a one dimensional box refers to a theoretical model in quantum mechanics where an electron is restricted to move in only one direction within a confined space, such as a potential well.

2. What is the significance of studying an electron confined in a one dimensional box?

Studying an electron confined in a one dimensional box allows us to understand the behavior of electrons in confined spaces and how they interact with their surrounding environment. This model is also helpful in understanding the properties of materials and can be applied in various fields, such as nanotechnology and material science.

3. How is the energy of an electron in a one dimensional box related to its wavelength?

The energy of an electron in a one dimensional box is directly proportional to its wavelength. This means that as the size of the box decreases, the energy of the electron increases, leading to shorter wavelength and higher frequency.

4. Can an electron confined in a one dimensional box have a specific energy level?

Yes, the energy of an electron confined in a one dimensional box is quantized, meaning it can only have certain discrete energy levels. The spacing between these energy levels is determined by the size of the box.

5. How is the behavior of an electron in a one dimensional box different from that of a free electron?

An electron in a one dimensional box is confined to a limited space and can only move in one direction, while a free electron can move freely in all directions. Additionally, the energy levels of an electron in a one dimensional box are discrete, while a free electron has a continuous range of energy levels.

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