Initial and final states of hydrogen atom

In summary: Then, I tried plugging in the other n's and getting 1.06, 1.11, 1.14. All of which are within the error of everything else.So, for the final state, I think it's either 5th order initially or it can change depending on the other n.
  • #1
vileoxidation
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Homework Statement



A hydrogen atom in an excited state emits a photon of wavelength 95nm. What are the initial and final states of the hydrogen atom? [Hint: you will need to make a reasonable guess of what is the final state. look at the energy of the photon and compare this energy with all the possible transitions in the hydrogen atom.]

Homework Equations



En=-E0/n^2
lambda=hc/(Ei-Ef)

The Attempt at a Solution



For the initial state, I set 95 = 1240/ (13.6-(-13.6/n^2)) and solved for n. I got 4.985, so I said it was 5th order initially. However, I think I may be doing this entirely wrong, as I cannot figure out how to get the final state.
 
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  • #2
The equation you solved is assuming the final state of the hydrogen atom was the ground state, n=1. Could the final state have been any other n?
 
  • #3
Does that change my equation for finding the initial state, or just for the final state? And for the final state, I tried to find E with E=hc/lambda, and then plug that in as the final energy, but that didn't work. I got something less then one.
 
  • #4
In general, the energy is 13.606*(1/nf^2-1/ni^2) where nf is the final state and ni is the intial state. What you did in your first attempt is basically the same as putting nf=1 and finding ni. And ni=5 looks good to me. Why couldn't nf be 2 or larger?
 
  • #5
Okay, so what I did now was set 95 = 1240 / [(-13.6/n^2)-(-13.6/25)] and solved for n, but I am getting something between 1 and 2, and not really very definitively either one. You can't be between energy states, so I know I must still be doing something wrong.

Thank you for all your help so far!
 
  • #6
Well, I get about 1.04 which is about as close as you can expect from the accuracy of everything else around.
 

FAQ: Initial and final states of hydrogen atom

1. What is the initial state of a hydrogen atom?

The initial state of a hydrogen atom is when the electron is in its ground state, or lowest energy level, and is bound to the nucleus by the electromagnetic force.

2. How does the initial state of a hydrogen atom change?

The initial state of a hydrogen atom can change when the electron absorbs energy and moves to a higher energy level, or when it interacts with other particles or fields, such as in a chemical reaction or under the influence of an external electric field.

3. What is the final state of a hydrogen atom?

The final state of a hydrogen atom is when the electron is in a stable energy level and is no longer interacting with other particles or fields. This can occur when the atom reaches its maximum energy level or when it undergoes a chemical reaction and forms a molecule.

4. How is the final state of a hydrogen atom determined?

The final state of a hydrogen atom can be determined by measuring the energy level of the electron, as well as any changes in its position or velocity. This can be done using spectroscopy techniques or by observing the atom's behavior in a chemical reaction.

5. Can the initial and final states of a hydrogen atom be predicted?

Yes, the initial and final states of a hydrogen atom can be predicted using the principles of quantum mechanics. By understanding the behavior of the electron and the forces acting on it, scientists can make accurate predictions about the atom's initial and final states.

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