Energy difference between spin up and spin down states

The energy difference between spin up and spin down states of hydrogen are important in understanding net magnetisation vector of tissue for magnetic resonance imaging.

Each hydrogen atom is formed by one proton and one orbiting electron. Because the atomic number is 1, it has a spin quantum number 1/2. Hence, the hydrogen proton can exist in two spin states: 'up' state and 'down' state.

The hydrogen proton has a positive charge and can also generate magnetic dipole moments. When a magnetic field is applied to a proton dipole, the dipole will either align 'parallel' or 'anti-parallel' relative to the direction of the magnetic field depending on its spin state.

The 'parallel' (low energy) and 'anti-parallel' (high energy) states have a difference in energy (ΔE) proportional to the magnetic field strength (B₀), gyromagnetic ratio (γ), and Planck constant (h):

• ΔE = γ * B₀ * h / (2 * π)

Boltzmann statistics can describe the ratio of the number of nuclei in the high (N_high) and low (N_low) energy states within a system as a function of the energy level difference (ΔE), temperature (T), and Boltzmann constant (k):

• N_high / N_low = e ^{- ΔE / (k * T)}