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Before you can understand how a drug works, you need to know its shape. In the 1940s, nobody could see the arrangement of atoms in a molecule like penicillin. Dorothy Hodgkin worked it out from patterns of X-ray spots, and went on to solve molecules that others thought too large to attempt. This post covers her life and work, how X-ray crystallography works and a Bragg's law calculation you can do yourself.
Who was Dorothy Hodgkin?
Dorothy Crowfoot was born in Cairo on 12 May 1910 and died on 29 July 1994, according to her Nobel Prize facts page. Her Nobel biography says she became interested in chemistry and crystals at about the age of 10. At her school in Beccles, she and one other girl were allowed to join the boys doing chemistry.
She studied chemistry at Somerville College, Oxford, from 1928 to 1932, then worked in Cambridge with J. D. Bernal. In 1934 she returned to Oxford, where she spent the rest of her career, and with help from Robert Robinson she raised money for X-ray apparatus. Her group worked for years in scattered rooms in the University Museum. She was elected a Fellow of the Royal Society in 1947.
How does X-ray crystallography work?
When X-rays pass through a crystal, the regularly spaced layers of atoms scatter them, and the scattered waves reinforce each other only in certain directions. The result is a pattern of spots. William and Lawrence Bragg shared the 1915 Nobel Prize in Physics "for their services in the analysis of crystal structure by means of X-rays". Their key result links the X-ray wavelength, the angle and the spacing between atomic layers:
nλ = 2d sin θ
Here n is a whole number, λ is the wavelength, d is the spacing between planes and θ is the angle between the incoming beam and the planes.
For simple salts this gives the structure fairly directly. For a large molecule there are a great many spots, and each must be measured and combined through long calculations.
Worked example: finding a layer spacing
X-rays of wavelength 0.154 nm give a first-order reflection at θ = 15.0°. Find the spacing d, then the angle of the second-order reflection.
First order (n = 1): d = λ / (2 sin θ) = 0.154 / (2 × 0.2588) ≈ 0.298 nm.
Second order (n = 2): sin θ = 2λ / 2d = λ/d = 0.154 / 0.2975 ≈ 0.518.
θ = sin⁻¹(0.518) ≈ 31.2°.
Notice that the second-order angle is not simply double the first. Sine is not linear.
Common mistakes to avoid:
Measuring θ from the wrong line. In Bragg's law θ is measured from the crystal planes, not from the normal to them.
Using 2θ as θ. Many instruments report the angle between the incoming and outgoing beams, which is 2θ. Halve it first.
Calculator in radians. sin 15 in radian mode is about 0.65, which gives a wrong d.
What did she discover?
According to the Nobel facts page, she determined the structure of penicillin in 1946 and of vitamin B12 in 1956. Her biography records that the penicillin work began in 1942, during the war, and the B12 work in 1948. The B12 structure, published in Nature in 1956, was described by the Nobel Foundation as having "the most complex structure of all vitamins". She received the 1964 Nobel Prize in Chemistry alone, "for her determinations by X-ray techniques of the structures of important biochemical substances".
Insulin was among the molecules she began studying in her early years at Oxford. Her group's structure, Structure of Rhombohedral 2 Zinc Insulin Crystals, was published in Nature in 1969 with ten authors. The Royal Society later published her biographical memoir, whose title records her Order of Merit.
Picturing molecules in three dimensions
If you struggle to picture shapes from flat diagrams, our post on visualising molecules gives practical ways to train that skill, and our guide to VSEPR and molecular shapes covers the shapes that come up in exams. When the idea behind a shape is the problem, the Fermi Concept Library covers every concept in chemistry and biology with its own lesson.
What can a student learn from how Hodgkin worked?
Pick hard problems on purpose. She chose molecules others thought too difficult, and solved them one by one.
Let others into the work. Her biography describes a research group of students and visitors from many universities. Problems this large are rarely solved alone.
Check the picture against the data. Every model had to fit the measured spots. In your own work, check every answer against the numbers you started with.
Practice this week: for the same planes (d = 0.298 nm), find the first-order angle with λ = 0.071 nm, and explain why the shorter wavelength gives a smaller angle.
