Calculating Energy for Exciting an Electron in a 1D Box

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In summary, the conversation is discussing the amount of energy needed to excite an electron to the first excited level in a 1-dimensional box with infinite potential on both sides. The energy was found to be 1.79*10^-17 in joules using the equation Delta(E)=(h'^2*(pi)^2*(n+1)^2)/2mL^2 - (h'^2*(pi)^2*n^2)/2mL^2, where h' is the reduced Planck's constant, n is the energy level, and L is the length of the box. The conversation also mentions the use of the Schrödinger equation and suggests looking into resources like the Wikipedia page on "Particle in
  • #1
kasse
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[SOLVED] Exciting an electron

An electron is in a 1-dimensional box with infinite potential on both sides. The length of the box is 1,0*10^-10 m. How much energy does it take to excite the electron to the first excited level?

Hm, I've got no idea how to solve this one...
 
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  • #2
Shouldn't you maybe figure out what the solutions of the schrodinger equation in such a box are?
 
  • #3
kasse said:
An electron is in a 1-dimensional box with infinite potential on both sides. The length of the box is 1,0*10^-10 m. How much energy does it take to excite the electron to the first excited level?

Hm, I've got no idea how to solve this one...
Have you looked at what your textbook has to say about this? What text are you using? Is this a calculus-based course?

(Aside: Dick, I've seen pre-calculus physics courses where the 1D infinite well is introduced without any reference to the SE. The derivation of energy eigenvalues involves using the de Broglie relation on allowed wavelengths for standing waves in the well.)
 
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  • #4
I used the Schrödinger equation and found the energy to be 1,79*10^-17. Is it correct?
 
  • #5
Is that in joules? What sort of an equation did you finally put numbers into? No matter what method you use (thanks, Gokul), you should find that there is more than one possible energy for the particle in the box to have. Do you have a formula for these possible energies? The problem is asking about the energy difference between two of them.
 
  • #6
Yes, in Joules.

I used the eq

Delta(E)=(h'*(pi)^2*(n+1)^2)/2mL^2 - (h'*(pi)^2*n^2)/2mL^2

where h' = h/(2*pi)
 
  • #7
Ok, then put n=1, right? So you get the difference between the n=2 state and the n=1 state. It looks fine to me. You really meant h'^2 in the equation, your answer is right so I'm guessing you did.
 
  • #8
yeah, h'^2.

This is just homework as a part of an intro course in nanotechnology. There's no book, only lectures. I think I should try to find some info on my own to improve my understanding.
 
  • #9
You could always flip through the wikipedia 'Particle in a box' entry for a quick intro. It's easy to find...
 

1. What is the formula for calculating the energy of an electron in a 1D box?

The formula for calculating the energy of an electron in a 1D box is:
E = (n^2 * h^2) / (8 * m * L^2), where n is the principal quantum number, h is Planck's constant, m is the mass of the electron, and L is the length of the 1D box.

2. How does the energy of an electron in a 1D box relate to its quantum state?

The energy of an electron in a 1D box is directly proportional to its quantum state. This means that as the quantum state (n) increases, the energy of the electron also increases.

3. Can the energy of an electron in a 1D box be negative?

Yes, the energy of an electron in a 1D box can be negative. This usually occurs when the quantum number (n) is zero, resulting in a negative energy value. However, this negative energy is still considered to be a valid energy state for the electron.

4. How does the length of the 1D box affect the energy of the electron?

The length of the 1D box (L) has a direct influence on the energy of the electron. As the length increases, the energy of the electron decreases. This is because a longer box allows for more possible energy levels for the electron to occupy.

5. What are some real-world applications of calculating the energy of an electron in a 1D box?

One real-world application is in the field of nanotechnology, where 1D boxes (nanowires) are used to confine electrons and control their energy levels. This is important for developing new technologies such as nanoscale transistors and sensors. Additionally, this concept is also applicable in quantum physics research and can help in understanding the behavior of electrons in different materials.

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