Final Lab Report 3 (AV and EK): Earth’s Field NMR

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.