# Earth’s Field NMR: first draft

Abstract

We performed an experiment to examine 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 thee 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 $$1852\pm18~Hz$$, 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 $$2.68\cdot 10^8~\frac{1}{s\cdot T}$$.

# Aims

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.

# Introduction

In 1945, Edward Purcell, Robert Pound and Henry Torrey worked on the development of radar during World War II at MIT Radiation Laboratory. Purcell, who led the group, had been successful in producing and detecting radio frequency power and in absorbing such radio frequency power. Purcell’s work led to the discovery of nuclear magnetic resonance (NMR).

Nuclear magnetic resonance is when nuclei in a magnetic field absorb and re-emit electromagnetic radiation. In order to measure NMR, an apparatus must be set at the resonance frequency, which depends on the strength of the magnetic field and the properties of the isotope of the atoms.

In our experiment, our apparatus (Fig.\ref{fig:TeachSpinApparatus}) studies the free precession of nuclear moments in the Earth’s magnetic field by detecting the collective precession of the nuclear magnetic moments in a particular sample.

\label{fig:TeachSpinApparatus} Earth’s field nuclear magnetic resonance (EFNMR1-A) apparatus.