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Aaronse_r
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[SOLVED] Hyperfine splitting of deuterium
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.
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
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 don't 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)
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 don't 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)
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