Hyperfine splitting of deuterium

  • Thread starter Aaronse_r
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  • #1
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[SOLVED] Hyperfine splitting of deuterium

Homework Statement


Calculate the wavelength of the photon emitted under a hyperfine transition in the ground state (n=1) of deuterium. Deuterium is a proton and a neutron in the nucleus, but still one electron. The spin of deuterium is 1.


Homework Equations



H prime=(magnetic moment)* B-field

mag moment of electron = (g-factor*e) / m_e
mag moment of deuterium = (g-factor*e) / (2m_d) g-factor for deut = 1.71

The Attempt at a Solution



I was able to solve up to the part where you get the expectation values...something like <S^2 - S(d)^2 - S(e)^2>. [the S(e) and S(d) are spin of electron and deuterium, sorry it's hard to read]

I dont know how to add the spins for the total spin vector though. My attempt at the spin states was this.

m = 1+1/2
m = 1/2
m = -1/2
m = -3/2

So S can be any of these values time hbar, and S^2 is hbar^2 *m(m+1)
 
Last edited:

Answers and Replies

  • #2
malawi_glenn
Science Advisor
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Use clebsh gordan tables.
 
  • #3
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Thank you i will try to make some sense of that thing!
 
  • #4
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S= 3/2 and 1/2
 
Last edited:
  • #5
pam
458
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You need s.S for s= spin 1/2 and S= spin 3/2.
Since J=s+S, you get 2s.S=J^2-S^2-s^2=j(j+1)-2-3/2.
 

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