Hydrogen Atom; energy state transitions

[hhhmortal]

Homework Statement

A hydrogen atom is initially in the state n=3. Subsequently it falls to its ground state with the emission of a photon. If the photon energy is ћω , then what is the ground state energy?

The Attempt at a Solution

I tried using E= h².n²/8ma².

and got -9ћω/8

I wasn't to sure how to go about with this question.

 

[Dick]

Uh, how did you get a negative ground state energy using that formula?

 

[hhhmortal]

Uh, how did you get a negative ground state energy using that formula?

Not too sure. I think that formula would just give you the energy of the level, but doesn't the electron in that level require that amount of energy to be ionised, hence the negative sign.

 

[Dick]

Not too sure. I think that formula would just give you the energy of the level, but doesn't the electron in that level require that amount of energy to be ionised, hence the negative sign.

You are right about that. And in fact, I think your answer is right. On the other hand the formula you gave for E is wrong. Why do you try and write down a clear derivation of your result?

 

[hhhmortal]

You are right about that. And in fact, I think your answer is right. On the other hand the formula you gave for E is wrong. Why do you try and write down a clear derivation of your result?

I'm not too sure, I think I just used that equation then I canceled out certain terms and multiplied it by ћω. This is wrong, but I can't find the right way of doing it.

 

[Dick]

I'm not too sure, I think I just used that equation then I canceled out certain terms and multiplied it by ћω. This is wrong, but I can't find the right way of doing it.

Start by finding the correct formula. The formula for the energy levels has an n^2 in the denominator, not the numerator. How can you be 'not to sure' of how you got the answer?!