Chapter 16, Problem 16.11P

Interpretation Introduction

Interpretation:

Suppose that the signal of a specific hydrogen nucleus appears 2200 Hz higher than that of the protons in TMS. If the NMR spectrometer uses a 7.046-T magnet, the chemical shift of that proton is to be calculated.

Concept introduction:

Chemical shift, abbreviated as the Greek letter $\text{δ}$ (delta), is a measure of the extent to which a signal’s frequency differs from that of a reference compound. The reference compound used for $\text{H}$ NMR spectroscopy is TMS. Formally, chemical shift, in units of parts per million (ppm), is defined by the mathematical expression

$\text{Chemical shift (ppm) = }\frac{{\text{ν}}_{\text{sample}}{\text{-ν}}_{\text{TMS}}}{{\text{ν}}_{\text{op}}}{\text{×10}}^{\text{6}}$.

Here, ${\text{ν}}_{\text{sample}}$ is the frequency of the signal of interest, ${\text{ν}}_{\text{TMS}}$ is the frequency of the signal from the protons in TMS, and ${\text{ν}}_{\text{op}}$ is the operating frequency of the NMR spectrometer, all of which are in units of hertz (Hz).