Earth’s Field NMR: first draft

Abstract

We examined the relationship between magnetization, polarizing field time, magnetic field and precession frequency using a 125 mL sample of water and the TeachSpin Earth’s Field NMR instrument. Through varying these different parameters, we could determine the Larmor precession frequency of protons within Earth’s field, spin-lattice relaxation time, and the gyromagnetic ratio for protons. We found the Larmor precession frequency to be \(1852\pm18~Hz\) corresponding to a local magnetic field of \(43.3\pm 0.3 \mu T\) due to Earth’s magnetic field, the spin-lattice relaxation time to be \(2.15\pm0.05~s\), and the gyromagnetic ratio to be \((2.65\pm0.04) \cdot 10^8~\frac{1}{s\cdot T}\), agreeing with the known value of \(2.68\cdot 10^8~\frac{1}{s\cdot T}\).

This experiment was designed to test the relationship between magnetization of protons, dependence on the polarizing field, and Larmor frequency by making a direct measurement of the gyromagnetic ratio and the field dependence of the precession frequency of protons in weak fields.

Nathanael A. Fortunealmost 2 years ago · Publicthis frequency is dependent on the value of the Earth’s magnetic field in your location, so you should indicate what you determined the field to be. For example, “a Larmor frequency of \(1852 \pm 18 \textrm{ [Hz]}\) corresponding to a local magnetic field of \(43.210 \mu T\) (made that number up) due to the Earth’s magnetic field. ”