Energy release and levels during electron transition

[ptownbro]

Homework Statement

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

 

[Borek]

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.

 

[ptownbro]

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

 

[Borek]

Have you heard names Bohr and Rydberg?

 

[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 textbook. Her's uses -2.18 x 10^-18, but online I see a 1.097 X 10^7 m^-1 constant.

 

[Borek]

These constants without units don't mean much, as energy can be expressed in many ways.

These pages contain everything you need (and then some):

https://en.wikipedia.org/wiki/Rydberg_formula

https://en.wikipedia.org/wiki/Bohr_model

 

[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.

 

[Borek]

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.

 

[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?

 

[Borek]

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

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

 

[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 JDid I qualify for the Nobel prize?

 

[Borek]

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 ΔE_electron > 0, if it goes to a lower n it emits energy, so the ΔE_electron < 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).

 

[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