mu_N = 3.15 *10^-8 eV/T
B = 2T
The transition energie delta E is calculated as: E(mJ = -3/2) – E(mJ= -1/2)
With:
E(-3/2)= -g * mu_N * B * (-3/2) = -1 * 3.15 * 10^-8 eV/T * 2T * (-3/2) = 9.45 * 10^-8 eV
E(-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 = 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

I= 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
I= 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