# NMR theory help

1. Feb 22, 2007

### gravenewworld

I'm trying to teach myself the theory behind NMR spectroscopy, but I am having some trouble with some pchem/physics concepts that I have never seen before.

The chapter I am currently on talks about the quantization of nuclear angular momentum. What I don't understand is, what is the difference between spin number (I) and nuclear spin angular momentum which my book gives as

P=h/2pi (I(I+1))^1/2

I have looked up what nuclear spin number (I) means on some physics websites and they state that I is the total angular momentum of the nuclei so I don't really understand what P really is if I is the total angular momentum of the nuclei.

Another term they talk about in the chapter is quantum number m_I (is this almost the same thing as the quantum number m_s for the electron?).

Given a magnetic field of strength B (in the z direction)a magnetic moment u would have an energy U given by

U=-u.B=-u_zB where u_z is the z component of u. They then go on to show that the energy is given by

U=-y(h/2pi)m_IB (y is the magnetogyric ratio) and state that there are 2I+1 values for m_I.

Could someone please explain P, I, and m_I ?? sorry for the equations, I don't know how to use latex.

Last edited: Feb 22, 2007
2. Feb 23, 2007

### Gokul43201

Staff Emeritus
I is simply a "quantum number" (just like the n, l, m that you are familiar with for an electron in a central potential; in this case, I is similar to the l quantum number, though it's closer to the electron spin quantum number s) - it is not the actual angular momentum. P is the actual angular momentum eigenvalue - it is what a single measurement of the total angular momentum will give (just as a measurement of the electron's orbital angular momentum, L, will tell you whether it is in an l=0,1,2,... state -ie: is an s, p, d... electron).

Just as I is a number that describes the quantization of the total angular momentum P, the number m_I describes the quantization of another observable, P_z (one component of the angular momentum vector). Yes, it is analogous to the m_s, which describes the quantization of S_z (any measurement of S_z will produce a result that is multiple of /hbar; this multiplication factor is designated m_s).

Last edited: Feb 23, 2007