Wavelengths due to electric dipole transitions

[brocq_18]

Homework Statement

Having problems with this subject. Given hydrogenic carbon, with binding energies of
490 eV (1s) 857.50 eV (2p) 925.54 eV (3p) 949.36 eV (4p). Find wavelengths of all lines due to electric dipole transitions between the levels. State which you expect to be strongest.

Homework Equations

I have extensively looked up electric dipoles in books and online and understand the subject competently, however the matter of electric dipole transitions has me stumped when I research it, and there is very little on the forums on it. Can anyone point me in the direction of some good sources please?

Thanks

Brocq

 

[Mike Pemulis]

Wikipedia article: "selection rules." First column of the table at the bottom.

 

[brocq_18]

Apologies, I've read into the selection rules more in depth than just as is shown on wikipedia, but still having some difficulties. Does this then mean I have to calculate the total angular momentum between each possible transition?:uhh:

 

[Solarflare201]

Apologies, I've read into the selection rules more in depth than just as is shown on wikipedia, but still having some difficulties. Does this then mean I have to calculate the total angular momentum between each possible transition?:uhh:

Hey, did you find the answer to this? I have a similar problem..

 

[brocq_18]

Hi, unfortunately not, I'm a little closer but still do not fully understand how to fulfill the problem...

 

[vela]

This might be more accessible to you than the Wikipedia page:

http://farside.ph.utexas.edu/teaching/qm/lectures/node64.html

 

[brocq_18]

This might be more accessible to you than the Wikipedia page:

http://farside.ph.utexas.edu/teaching/qm/lectures/node64.html

Hi Vela, appreciate your help. I have gotten much further with this now, just having slight difficulties with the following problem which asks to find the corresponding wavelengths from hydrogen like oxygen.

Having attained some advice I have been told all that is needed is to scale up the Z value in relation to oxygen. Does this mean I just increase the wavelength values by a 1/3, to represent the increased difference in Z value between carbon and oygen...?

Solarflare201, I have messaged you with details of what I have done so far.

 

[vela]

No, that's not correct. You know that$$E_\gamma = \frac{hc}{\lambda} = E_i - E_f$$where λ is the wavelength of the emitted photon, and E_f and E_i are the energy of the final and initial state of the electron. How do the energies scale with Z?

 

[brocq_18]

Sorry, my apologies, what I meant was the Z values are scaled up in squares...but I cannot visualise where I go from here with the data I have...

 

[vela]

So the energy goes as Z². That means if Z doubles, the energies change by a factor of 4.

Now how does wavelength scale with energy? For example, if you double the energy of a photon, what happens to the wavelength?

 

[brocq_18]

Wavelength is inversely proportional to energy...Ok, so, as the atomic number of oxygen is higher, cleary more energy is released when the electron drops between shells. This would mean shorter wavelengths. As Z increases by 1/3 from carbon to oxygen, am I correct in assuming the wavelengths increase by 1/9..?

 

[vela]

Not quite. By what factor does Z increase going from C to O? It's not 1/3 because that would cause Z to decrease.

 

[brocq_18]

Unconfidently I'll say a factor of 2..

 

[vela]

6*2 = 8?

 

[brocq_18]

4/3, so this is the factor we increase to get from C to O, would we then take the inverse of the wavelengths, that being 3/4? That can't be correct because it doesn't take into account the square function, so would I apply this to the inverse and multiply the wavelengths? I hope that's right..

 

[vela]

You don't have to guess. What does the math tell you?

 

[brocq_18]

As Eγ=hc/λ I take the inverse of the increasing factor, and in order to satisfy the square, this would also be squared, and multiplied with the corresponding wavelenghts, in order to get the values respective to oxygen! :)

 

[vela]

Sounds good!

 

[brocq_18]

Thank you for your help Vela, and patience. This helps my comprehension on the matter a lot!