mu_N = 3.15 *10^-8 eV/T, B = 2T
Transition energie delta E = E(mJ = -3/2) – E(mJ= -1/2)
E(mJ = -3/2)= -g * mu_N*B* (-3/2) = -1 * 3.15 *10^-8 eV/T * 2T * (-3/2) =9.45*10^-8 eV
E(mJ= -1/2)= -g * mu_N*B* (-1/2) = -1 * 3.15 *10^-8 eV/T * 2T * (-1/2) = 3.15*10^-8 eV
delta E = 9.45*10^-8 eV – 3.15*10^-8 eV = 6.3*10^-8 eV

With the hyperfine interaction : here mu = g *mu_N*I
A = (mu *B_hf)/(I*J) = (g * mu_N * I * B_hf)/(I*J) = (3.15 * 10^-8 eV/T * 10 T) / *(3/2) A = 2.1 10^-7 eV

mI= 1/2 : E(mJ=-3/2) = – 3.15*10^-8 eV + 2.1 10^-7 eV * (1/2) *(-3/2) = -1.8 * 10^-7 eV
mI= 1/2 : E(mJ=-1/2) = – 3.15*10^-8 eV + 2.1 10^-7 eV * (1/2) *(-1/2) = -0.84 *10^-7 eV

delta E = 1.05 10^-7 eV