Characteristic Spectrum and the K-alpha line

[Baddum12]

I have just finished a junior-level lab assignment in which we used X-ray diffraction to determine the lattice constants of unknown materials. In the theory section of the lab write-up, it briefly explains the K-alpha doublet of the characteristic spectrum. I understand that it is the result of a vacancy in the K shell being filled from the L shell, and I understand that the two lines (K_α1 and K_α2) can appear as a single, unresolved line which is taken as the weighted average of the two lines. What I don't understand is why the K_α1 line is always twice as strong as the K_α2 line. I have read through the section on the characteristic spectrum in {Cullity, B.D. Elements of X-Ray Diffraction. 3ed. Prentice Hall, 2001} and I am still a little confused. Is this just an experimentally observed fact?

 

[Vagn]

I have just finished a junior-level lab assignment in which we used X-ray diffraction to determine the lattice constants of unknown materials. In the theory section of the lab write-up, it briefly explains the K-alpha doublet of the characteristic spectrum. I understand that it is the result of a vacancy in the K shell being filled from the L shell, and I understand that the two lines (K_α1 and K_α2) can appear as a single, unresolved line which is taken as the weighted average of the two lines. What I don't understand is why the K_α1 line is always twice as strong as the K_α2 line. I have read through the section on the characteristic spectrum in {Cullity, B.D. Elements of X-Ray Diffraction. 3ed. Prentice Hall, 2001} and I am still a little confused. Is this just an experimentally observed fact?

For K_α1 the total angular momentum of the initial state is 3/2, this has states with J_z components of 3/2,1/2,-1/2,-3/2. In comparison the inital states for k_α2 emission have a total angular momentum of 1/2 which has J_z values of 1/2,-1/2. Thus there are twice as many states which for the electron to decay to by emitting K_α1 than K_α2.

 

[Baddum12]

For K_α1 the total angular momentum of the initial state is 3/2, this has states with J_z components of 3/2,1/2,-1/2,-3/2. In comparison the inital states for k_α2 emission have a total angular momentum of 1/2 which has J_z values of 1/2,-1/2. Thus there are twice as many states which for the electron to decay to by emitting K_α1 than K_α2.

Thanks a lot, Vagn, that is actually pretty straight-forward. Cheers!