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An MRI scanner can show the inside of a knee or a brain without X-rays. Most students know it uses "a big magnet", but not why a magnet should produce a picture at all. The answer came from two people in the early 1970s: a chemist in New York and a physicist in Nottingham. This post explains their idea with real numbers and what their careers say about how science moves.
What did Lauterbur and Mansfield win the Nobel Prize for?
The Nobel Assembly's 2003 press release awarded the Physiology or Medicine prize jointly to Paul C. Lauterbur and Peter Mansfield "for their discoveries concerning magnetic resonance imaging". It credits Lauterbur with discovering that gradients in the magnetic field make it possible to build two-dimensional pictures, and Mansfield with showing how the signals could be analysed mathematically and how very fast imaging could be achieved.
The physics underneath was older. The same release notes that nuclear magnetic resonance was demonstrated for protons in 1946 by Felix Bloch and Edward Purcell, who received the 1952 Nobel Prize in Physics. For decades NMR was a tool for working out the structure of molecules in chemistry labs. It was not yet a way to see where things were.
How does a magnetic field gradient turn a signal into a picture?
A hydrogen nucleus in a magnetic field absorbs and re-emits radio waves at one particular frequency, and that frequency is proportional to the field. For the proton, NIST lists the constant as 42.577 MHz per tesla (CODATA 2022).
Here is the worked example.
In a 1.5 T scanner: f = 42.58 MHz/T × 1.5 T ≈ 63.9 MHz. That is a radio frequency, with a wavelength of about 3 × 10^8 / 63.9 × 10^6 ≈ 4.7 m.
Now add a small gradient, so the field rises steadily across the body. Take a sample gradient of 10 mT per metre. Two points 1 cm apart then differ in field by 0.010 T/m × 0.01 m = 1.0 × 10^-4 T.
Their resonance frequencies differ by 42.58 × 10^6 Hz/T × 1.0 × 10^-4 T ≈ 4,260 Hz.
So if the scanner hears a signal at 63.9 MHz plus 4.26 kHz, it knows the hydrogen sits 1 cm further along the gradient. Frequency has become position. That is Lauterbur's insight in one line.
The 10 mT/m gradient above is a sample number chosen to keep the arithmetic clean; the 42.58 MHz/T constant is the measured value.
Why does MRI see soft tissue so well?
The Nobel press release explains that water makes up about two thirds of human body weight, and that tissues and organs differ in water content. Many diseases change that water content, and the change shows up in the image. The release adds that MRI uses no ionising radiation, and that it is especially valuable for the brain and spinal cord, because nearly all brain disorders change water content. The release also notes that people with pacemakers or magnetic metal in the body cannot be scanned, because of the strong field.
How did Lauterbur get the idea?
In his Nobel biography, Lauterbur describes an unlikely route. In 1971 he was briefly running a small NMR equipment company near Pittsburgh. A post-doc arrived to measure NMR signals from tumour-bearing rats. The differences between tissues were real, but the method required killing the animals, which troubled him. That evening, he writes, he realised there might be a way to locate the precise origins of NMR signals and so form an image in two or even three dimensions.
He published his demonstration in Nature in 1973, in Image formation by induced local interactions. The press release describes it: he imaged tubes of ordinary water surrounded by heavy water, two liquids no other imaging method could tell apart.
What did Mansfield add?
Mansfield, working at Nottingham, developed ways to analyse the signals mathematically and turn them into images efficiently; his 1973 paper with Grannell, NMR "diffraction" in solids?, came the same year. He also proposed extremely fast gradient switching, known as echo-planar imaging. The press release says this became useful in clinical practice about a decade later.
Mansfield's path is worth knowing. His Nobel biography records that he failed to get a grammar school place, left school at 15 to work as a printer's assistant, then took a job at a rocket propulsion department. He studied for A-levels part time and entered Queen Mary College, London in 1956. His undergraduate project was to build a portable NMR spectrometer to measure the Earth's magnetic field.
What can a student take from their way of working?
Look for the variable that carries information. Lauterbur's step was to make frequency depend on position on purpose. In any physics problem, ask which quantity changes with the thing you want to find.
Do the arithmetic early. Checking that 1 cm gives a few kilohertz, which electronics can measure, is how you know an idea is practical.
Borrow across fields. NMR was a chemist's tool; the use was medical. Both laureates moved between subjects.
Late starts are not dead ends. Mansfield left school at 15 and still built the methods behind modern scanners.
If the link between magnetic fields and frequency feels abstract, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. For the radio side of the story, our guide to the electromagnetic spectrum places 64 MHz among the radio waves you study in Class 12.
Try it now: work out the resonance frequency in a 3 T scanner and the frequency shift across 2 mm with the same sample gradient.
