g = 1, I = 1/2, B_0 = 2T, mu = 3.15 * 10−8 eV/T

energy level: E = -g * mu * m_j * B_0
E = -g * mu * m_j * B_0 + (A * m_I * m_J)

Hyperfine constant: A = mu * B_hf / I * J = 3.15 * 10−8 eV/T * 10 T / (1/2) *(3/2) = 4.2 * 10-7 eV

Without hyperfine interactions (m_j = -3/2, -1/2): deltaE = E(-3/2) – E(-1/2) = -1 * -g * mu * B_0 = 6.3*10-8 eV
(m_j = -1/2, +1/2): deltaE = E(-1/2) – E(1/2) = -1 * -g * mu * B_0 = 6.3*10-8 eV

With hyperfine interactions (m_j = -3/2, -1/2): deltaE = 6.3*10-8 eV + (4.2 * 10-7 eV * (-1/2) * (-3/2) = 3.213*10-6 eV
(m_j = -1/2, 1/2): deltaE = 6.3*10-8 eV + (4.2 * 10-7 eV * (-1/2) * (1/2) = 9.87*10-7 eV