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No hyperfine interaction:
\Delta E=g*(m_{I+}-m_{I-})*\mu_B*B_0=1*(1/2)(1/2-(-1/2))*9*10^(-24)(J/T)*2T=9*10^(-24)T
Hyperfine interaction from m_J=-3/2 to m_J=-1/2:
\Delta E=(\mu_N*B_{hf}/(I*J))*m_I*(m_{J+}-m_{J-})=(5*10^(-27)(J/T)*10T/((1/2)*(3/2)))*(3/2)*(-1/2-(-3/2))=2*10^(-25)J
Hyperfine interaction from m_J=-1/2 to m_J=1/2:
\Delta E=(\mu_N*B_{hf}/(I*J))*m_I*(m_{J+}-m_{J-})=(5*10^(-27)(J/T)*10T/((1/2)*(3/2)))*(1/2)*(1/2-(-1/2))=2*10^(-25)J=(2/3)*10^(-25)J
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