Warning: Although we have described two pure states for the nucleus (spin-up and spin-down), it is incorrect to infer that spins physically reside only in one of these two states or that they "flip" from one state to another. See the next Q&A for a more complete discussion.
where h is Planck's constant whose value is approximately 6.626 x 10-34 Joule-sec. Planck's constant reflects the granularity of the subatomic world and the fact that energy is released or absorbed only in discrete packets or quanta.
The energy gap (ΔΕ) between two nuclear spin states scales directly with magnetic field strength and is given by the Zeeman equation:
ΔΕ = γ h Bo
where γ is called the gyromagnetic ratio, a constant specific to a particular nucleus. For the ¹H nucleus, the value of γ is 42.58 MHz/Tesla.
The Planck relation and Zeeman equation may be combined, producing an interesting and important result that will look familiar to those with prior exposure to MRI:
fo = γ Bo
If you don't understand everything right now, don't worry. We will have much, more more to say about the Larmor equation in later Q&A's!
Advanced Discussion (show/hide)»
Because the electron has a negative gyromagnetic ratio (γ), its magnetic moment points opposite to the direction of its spin. The spin-up state |+½> is therefore the higher energy level. Also, the direction of electron precession with respect to Bo is actually opposite that of the hydrogen proton,
"Nuclear Magnetic Resonance." Wikipedia, The Free Encyclopedia.
Cresser JD. Particle spin and the Stern-Gerlach experiment. Lecture notes in quantum mechanics, Chapter 6, from: physics.mq.edu.au/~jcresser/Phys301.html (27 April 2009)
What is spin?
How do you predict the value of nuclear spin (I) based on the number of protons and neutrons?
Where does the energy come from to keep the precession going?