Photo 51: X-Ray Diffraction & the Discovery of DNA

Helix Geometry

Pitch P (rise per turn) 34.0 Å

Backbone radius r₀ 9.0 Å

Strand stagger Δ/P 0.375

Diffraction Readouts

Layer-line spacing 1/P

0.0294 Å⁻¹

Base pairs / turn (h=3.4 Å)

10.0

4th layer-line intensity

≈ 0 (missing)

How it works

In 1952 Rosalind Franklin's "Photo 51" showed the X-ray diffraction pattern of a B-DNA fibre: a cross ("X") of spots. Fibre diffraction from a helix follows the Cochran–Crick–Vand theory — the amplitude scattered onto the l-th layer line at radial distance R is a Bessel function of the first kind:

A_l(R)  =  J_l(2π r₀ R)
I_l(R)  =  |A_l(R)|² · cos²(π l Δ/P)   for a 2nd strand offset by Δ along the axis
layer lines spaced at 1/P along the meridian (Bragg's law on the fibre axis)

Each order J_l has its first maximum further from the origin as |l| grows, so stacking layer lines l = 0,±1,±2,… produces the diagonal arms of the X — exactly what appears on the plate. The cos² term is the interference between the two backbones of a double helix: when the axial stagger Δ is about 3/8 of the pitch P (true for B-DNA, 10 bp/turn), cos²(πl·0.375) collapses to ≈0 at l = 4 — the real, famous "missing" 4th layer line. Franklin's measurement of it, and of the 34 Å repeat, is what let Watson and Crick deduce two antiparallel strands, 10 bases per turn, wound around a common axis.

Pitch P — vertical repeat distance of one full helix turn; sets how closely the horizontal layer lines are packed (spacing = 1/P).
Radius r₀ — helix diameter; stretches the Bessel argument, widening the X's opening angle.
Stagger Δ/P — axial offset between the two backbones; drag it away from 0.375 and the 4th layer line reappears, showing why that one missing spot was such strong evidence.
B-DNA / A-DNA presets — B-DNA (P≈34 Å, r₀≈9 Å, the wet, biologically dominant form Franklin photographed) vs A-DNA (shorter, fatter, dehydrated form she also identified — the two forms she was famous for telling apart).

Backbone strand 1 Backbone strand 2 Base-pair rungs

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Photo 51: X-Ray Diffraction & the Discovery of DNA's Double Helix