# Energy release and levels during electron transition

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1. Nov 17, 2015

### ptownbro

1. The problem statement, all variables and given/known data

Been looking but can't seem to find any comprehensive help on this.

In the Hydrogen atom, what energy is associated with these electron energy transitions:
a) N = infinity to N=2?
b) N = infinity to N=3?
c) N = 4 to N=2?
d) N = 5 to N=6?

I don't have any relevant formulas to start from or know where to start to give my attempt.

Any help appreciated.

thanks

Last edited: Nov 17, 2015
2. Nov 17, 2015

### Staff: Mentor

There is no general formula and the question - as asked - has no definite answer.

Unless it is asked in the context of hydrogen like single electron Bohr atom, then it is trivial.

3. Nov 17, 2015

### ptownbro

Sorry, I edited the question to make it more clearer (hopefully). It relates to the Hydrogen atom.

4. Nov 17, 2015

### Staff: Mentor

Have you heard names Bohr and Rydberg?

5. Nov 17, 2015

### ptownbro

I have heard of Bohr and just read a little bit about Rydberg, but I can't seem to apply what I've read to this simple version. Also, I'm getting different constants than what was given in my daughter's text book. Her's uses -2.18 x 10^-18, but online I see a 1.097 X 10^7 m^-1 constant.

6. Nov 17, 2015

### Staff: Mentor

7. Nov 17, 2015

### ptownbro

I also added a more complicated question somewhat related o this, but I need to understand this basic part first I believe. All examples I've found use a given "Electron Volts" but my daughter's questions do not. So having hard time to translate what I've read to this.

8. Nov 17, 2015

### Staff: Mentor

Ev is just an energy unit, just like Joule. m-1 is not an energy unit, but it can be used to express the wavelength of the emitted photon, so in this case it is directly related to the energy. As it is wavelength that is easy to observe, we often use it in this context.

9. Nov 17, 2015

### ptownbro

Could you maybe give me the question in a restated way as an example with the piece missing so we could get a hint of where to look?

10. Nov 17, 2015

### Staff: Mentor

Simply plug both n values (initial and final) into the Rydberg formula.

1/∞2 can be problematic - but is it much different from zero?

11. Nov 17, 2015

### ptownbro

Her teacher does't do a good job of explaining and leaves you to have to guess a lot. So, sorry I don't have a clearer question.

Anyway, if I understand this.... Please confirm or correct where I'm wrong. =D

There different Ryberg constants that can be used depending on the context of the equation.

If related to the inverse of wavelength, you use R=1.097 X 10^7 m^-1
If related to the change in energy, you use R= -2.18 x 10^-18 J

In the question, it asked: In the Hydrogen atom, what energy is associated with these electron energy transitions?

Given, what I highlighted, I can infer then I must use the R=2.18 x 10^-18 J constant and the following formula:

ΔE = R ( 1 / n2^2 - 1 / n2^2)

Given what you said about infinity and going through her notes again, N=infinity is zero (or effectively ignored).

a) N = infinity to N=2?

ΔE = R ( 1 / n2^2 ) = -2.18 x 10^-18 J * (1 / 4) = -0.545 x 10^-18 J

b) N = infinity to N=3?

ΔE = R ( 1 / n2^2 ) = -2.18 x 10^-18 J * (1 / 9) = -0.242 x 10^-18 J

c) N = 4 to N=2?

ΔE = R ( 1 / n2^2 - 1 / n2^2) = -2.18 x 10^-18 J * (1 / 4 - 1 / 16) = -0.409 x 10^-18 J

d) N = 5 to N=6?

ΔE = R ( 1 / n2^2 - 1 / n2^2) = -2.18 x 10^-18 J * (1 / 36 - 1 / 25) = +0.027 x 10^-18 J

Did I qualify for the Nobel prize?

12. Nov 17, 2015

### Staff: Mentor

Question doesn't ask about "energy change", but about "energy associated" with the transition. Thus I would report all values as positive.

Sign would make the difference if you were asked about the change of the energy of the electron (to go to a higher n it needs to absorb energy, so ΔEelectron > 0, if it goes to a lower n it emits energy, so the ΔEelectron < 0). Surroundings would have exactly the same change of energy, but with the opposite sign (technically it is the photon that is either absorbed from the surroundings, or emitted to the surroundings, but speaking about change of energy of a photon that didn't exist before emission is rather clumsy).

13. Nov 17, 2015

### ptownbro

Excellent. Thank you.

So to correct what I did in each above, I should use R=+2.18 x 10^-18 J in each (instead of R=-2.18 x 10^-18 J like I did)

Thanks again