Nuclear Magnetic Resonance: How MRI and NMR Work

Nuclear magnetic resonance is one of the most powerful ways to work out the structure of a molecule. A single NMR spectrum can tell a chemist how many different types of hydrogen atom a molecule contains, how many of each there are, and which ones sit next to each other. In medicine, the same physics produces detailed pictures of the inside of the human body without X-rays: the MRI scan.

This article explains how NMR works and what information a spectrum contains.

Nuclear spin

Some atomic nuclei behave like tiny spinning magnets. This property is called nuclear spin. Nuclei with an odd number of protons or neutrons have spin and are “NMR active”. The most important in chemistry are:

• ¹H (the ordinary hydrogen nucleus, a single proton), 99.98% of natural hydrogen
• ¹³C, only about 1.1% of natural carbon (¹²C has no spin and is invisible to NMR)
• Others: ¹⁹F, ³¹P, ¹⁵N

What happens in a magnetic field

With no magnetic field, nuclear spins point in random directions and all have the same energy.

In a strong external magnetic field, a spin-½ nucleus like ¹H can line up in two ways:

• aligned with the field (lower energy)
• opposed to the field (higher energy)

The energy difference between these two states, ΔE, is small, and it’s proportional to the strength of the magnetic field. It corresponds to radio frequency radiation.

When the sample is exposed to radio waves of exactly the right frequency, nuclei absorb energy and “flip” from the lower to the higher state. That’s the resonance in nuclear magnetic resonance. When they relax back, the signal is detected.

Modern NMR spectrometers use superconducting magnets with fields of about 7–23 tesla, hundreds of thousands of times stronger than Earth’s magnetic field. They’re usually described by the resonance frequency of ¹H in the magnet: 300 MHz, 400 MHz, 600 MHz and even over 1 GHz.

Chemical shift: why NMR tells you about structure

If every hydrogen nucleus absorbed at exactly the same frequency, NMR would be useless for chemistry. But they don’t.

The electrons around a nucleus also respond to the magnetic field, creating a small opposing field. This shields the nucleus, so it experiences a slightly weaker field and absorbs at a slightly lower frequency.

• Hydrogens near electronegative atoms (O, N, halogens) have electron density pulled away from them. They’re deshielded and absorb at higher frequency.
• Hydrogens in electron-rich environments are shielded and absorb at lower frequency.

So hydrogens in different chemical environments absorb at different frequencies. The position of each signal is its chemical shift, δ, measured in parts per million (ppm) relative to a reference compound.

The reference: TMS

The standard reference is tetramethylsilane (TMS), Si(CH₃)₄, which is assigned δ = 0 ppm. It’s used because:

• all 12 hydrogens are in the same environment, giving a single sharp peak
• silicon is less electronegative than carbon, so the hydrogens are strongly shielded, and the TMS peak appears at the far right, away from most other signals
• it’s inert, non-toxic in small amounts and volatile (easily removed)

Chemical shift in ppm is independent of the spectrometer’s field strength, so spectra from different instruments can be compared directly.

Typical ¹H chemical shifts

Type of hydrogen	Approximate δ (ppm)
R–CH₃ (alkyl)	0.7–1.2
R–CH₂–R	1.2–1.5
H–C–C=O (next to carbonyl)	2.0–2.6
H–C–N	2.3–3.0
H–C–O (alcohols, ethers, esters)	3.3–4.3
H–C=C (alkene)	4.5–6.5
Aromatic H (on benzene ring)	6.5–8.5
Aldehyde (–CHO)	9.5–10.0
Carboxylic acid (–COOH)	10–12
R–OH, R–NH	variable, often 1–5 (broad)

Exam data sheets give similar tables.

What a ¹H NMR spectrum tells you

A ¹H NMR spectrum provides four types of information:

1. Number of signals → number of different hydrogen environments.
2. Chemical shift → the type of environment (what the hydrogen is near).
3. Integration (relative peak area) → the relative number of hydrogens in each environment.
4. Splitting pattern → the number of hydrogens on neighbouring carbons (the n + 1 rule: n neighbouring H give n + 1 peaks).

Example: ethanol, CH₃CH₂OH

• Three environments: CH₃, CH₂ and OH → three signals
• CH₃ at about 1.2 ppm, split into a triplet (2 neighbouring H)
• CH₂ at about 3.7 ppm, split into a quartet (3 neighbouring H); shifted downfield because it’s next to O
• OH at about 2–5 ppm, a broad singlet (often not split, because the OH proton exchanges rapidly)
• Integration ratio 3 : 2 : 1

Working out full structures from these four types of information is a core skill in advanced organic chemistry.

¹³C NMR

¹³C NMR works on the same principle but detects carbon-13 nuclei. Because only 1.1% of carbon is ¹³C, it’s less sensitive and spectra take longer. Spectra are usually “decoupled”, so each different carbon environment appears as a single line. The number of lines tells you how many different carbon environments there are, and chemical shifts range over about 0–220 ppm (C=O carbons appear at 160–220 ppm).

Deuterated solvents

Samples are dissolved in solvents where hydrogen is replaced by deuterium (²H), such as CDCl₃. Deuterium absorbs at a completely different frequency, so the solvent doesn’t swamp the spectrum. The deuterium signal is also used by the instrument to keep the magnetic field stable.

D₂O shake: adding a drop of D₂O to an NMR sample swaps OH and NH hydrogens for deuterium. Their peaks disappear, which confirms which signal is from O–H or N–H.

MRI: NMR inside the body

Magnetic resonance imaging uses the same physics, detecting mainly the ¹H nuclei in water and fat in the body. The patient lies inside a large superconducting magnet (typically 1.5 or 3 tesla). Magnetic field gradients make the resonance frequency depend on position, so the signals can be decoded into 3D images.

Different tissues give different signals because their water content and how quickly their nuclei relax (return to equilibrium) differ. That lets MRI distinguish soft tissues, such as brain, muscle, cartilage and tumours, far better than X-rays can. MRI uses no ionising radiation.

The “nuclear” was dropped from the name for medical use, partly because patients associated the word with radioactivity, which isn’t involved.

A short history

• 1938: Isidor Rabi detects nuclear magnetic resonance in molecular beams (Nobel Prize in Physics, 1944).
• 1946: Felix Bloch and Edward Purcell independently detect NMR in liquids and solids (Nobel Prize in Physics, 1952).
• 1950s–1960s: chemical shift and splitting are discovered, and NMR becomes a key tool for chemists.
• 1970s: Paul Lauterbur and Peter Mansfield develop methods for MRI imaging (Nobel Prize in Physiology or Medicine, 2003). Richard Ernst develops Fourier transform NMR (Nobel Prize in Chemistry, 1991).
• 2002: Kurt Wüthrich wins the Nobel Prize in Chemistry for using NMR to determine protein structures in solution.

Key takeaways

• Nuclei with spin, such as ¹H and ¹³C, have two energy states in a magnetic field and absorb radio waves when they flip between them.
• Electrons shield nuclei; hydrogens near electronegative atoms are deshielded and appear at higher chemical shift.
• Chemical shifts are measured in ppm relative to TMS (δ = 0).
• ¹H NMR gives the number of environments, their type, their relative numbers of H, and neighbouring H (splitting).
• MRI uses the same physics on water and fat in the body to produce detailed images without ionising radiation.