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Without hyperfine interaction:
Delta_E=g_J*u_B*B_0=0.8*57.88meV/T*2T=92.608meV
The exercise mentions g=1 but does not define which g and the picture mentions g_J=0.8. 0.8 was used.with hyperfine interaction
Correction on terms:
A*m_I=g*u_N*B_hf*m_I*m_J/J
Former m_J=-3/2 -> -1/2:
+1/2 transition:
1*57.88meV/T*10T*0.5*-1.5/1.5-1*57.88meV/T*10T*0.5*-0.5/0.5=-57.88meV/T*10T*0.5+57.88meV/T*10T*0.5=0
Obviously something is wrong here and I suspect it stems from my lack of understanding regarding calculating the hyperfine correct. I addressed this while watching in one of the questions I sent.
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