Energy difference between spin up and spin down states
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 (Nhigh) and low (Nlow) energy states within a system as a function of the energy level difference (ΔE), temperature (T), and Boltzmann constant (k):
- Nhigh / Nlow = e - ΔE / (k * T)
- 1. Atta-ur-Rahman T. Nuclear magnetic resonance. New York: Springer-Verlag, 1986.
- 2. Bushberg J, Seibert J, Leidholdt E, Boone J. The Essential Physics of Medical Imaging. Lippincott Williams & Wilkins, 2011.