How many hertz from the TMS signal is the signal occurring at 2.0 ppm

a. in a 300 MHz spectrometer?

b. in a 500 MHz spectrometer?

The interaction of radio waves of the electromagnetic spectrum with the nucleus of an atom is called NMR spectroscopy. A nucleus is NMR active if it has an odd atomic number or mass number.

The instrument used to study these interactions is called a spectrometer. The molecules are kept in a strong magnetic field during which the NMR nuclei behave like magnets. Then, when the system is irradiated with radiowaves, and nuclei resonate at specific frequencies.

The frequencies at which each nucleus resonates are recorded as peaks in an NMR spectrum. The intensity of the peak represents the number of nuclei. The frequencies of each nucleus in a compound are compared using a reference which is tetramethylsilane (TMS).

The operating frequency of a spectrometer is the frequency at which a hydrogen atom resonates in the instrument and depends on the strength of the magnet used in it. The chemical shift is the resonant frequency of a signal relative to the standard and is independent of the operating frequency of the spectrometer.

The chemical shift of a signal is calculated as the distance of the signal from the TMS signal divided by the operating frequency of the spectrometer.

Therefore, the distance between a signal and TMS signal in Hz can be calculated as:

$\mathrm{Downfield}\mathrm{from}\mathrm{TMS}\left(\mathrm{Hz}\right)=\mathrm{operating}\mathrm{frequency}\left(\mathrm{MHz}\right)\times \mathrm{chemical}\mathrm{shift}\left(\mathrm{ppm}\right)$

a. The chemical shift of the signal is 2.00 ppm, and the operating frequency of the spectrometer is 300 MHz.

Therefore, the distance from the TMS signal is

$\begin{array}{c}\mathrm{Downfield}\mathrm{from}\mathrm{TMS}=300\mathrm{MHz}\times 2.00\mathrm{ppm}\\ =600\mathrm{Hz}\end{array}$

The distance from the TMS signal is 600 Hz.

b. The chemical shift of the signal is 2 ppm, and the operating frequency of the spectrometer is 500 MHz.

Therefore, the distance from the TMS signal is:

$\begin{array}{c}\mathrm{Downfield}\mathrm{from}\mathrm{TMS}=500\mathrm{MHz}\times 2.00\mathrm{ppm}\\ =1000\mathrm{Hz}\end{array}$

The distance from the TMS signal is 1000 Hz.