Change in photon energy

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Without hyperfine interactions we have:
E=-g*mu_N*B_0*m_J with mu_N=3.15*10^-8eV/T
so we have
E(-3/2)=-1*3.15*10^-8 eV/T * 2 T * -3/2 = 9.45*10^-8 eV
E(-1/2)=-1*3.15*10^-8 eV/T * 2 T * -1/2 = 3.15*10^-8 eV
E(+1/2)=-1*3.15*10^-8 eV/T * 2 T * +1/2 = -3.15*10^-8 eV

so
E(m=-3/2)-E(m=-1/2)= 6.3 * 10^-8 eV and E(m=-1/2)-E(m=+1/2)= 6.3 * 10^-8 eV

With hyperfine interactions we have
E=-g*mu_N*B_0*m_I + A*m_J*m_I with A=mu_N*Bhf/I*J = 3.15*10^-8 eV/T*10 T / (1/2)*(3/2) =42*10^-8 eV
so we have
E(-3/2)=-1*3.15*10^-8 eV/T * 2 T * -3/2 + 42*10^-8 eV * (1/2)*(-3/2)= -22.05*10^-8 eV
E(-1/2)=-1*3.15*10^-8 eV/T * 2 T * -1/2 + 42*10^-8 eV * (1/2)*(-1/2) = -7.35*10^-8 eV
E(+1/2)=-1*3.15*10^-8 eV/T * 2 T * +1/2 + 42*10^-8 eV * (1/2)*(+1/2)= +7.35*10^-8 eV

E(m=-3/2)-E(m=-1/2)= -14.7 * 10^-8 eV and E(m=-1/2)-E(m=+1/2)= -14.7 * 10^-8 eV

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