A synthetic filament is studied by fibre diffraction (the same layer-line method used…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Biophysics & Medical Physics · Crystal structure, bonding and diffraction

Forces, Machines and Signals, Ch Seeing molecules: diffraction, cryo-electron microscopy and fluorescence

Problem

A synthetic filament is studied by fibre diffraction (the same layer-line method used for B-DNA). On the pattern, successive layer lines are spaced 0.15 nm−10.15\,\mathrm{nm^{-1}} apart along the fibre axis, and a strong meridional (on-axis) reflection appears at 1.5 nm−11.5\,\mathrm{nm^{-1}}. On the innermost layer line (ℓ=1\ell = 1), the first side-maximum of the Bessel function J1J_1 appears at a radial distance qr=0.32 nm−1q_r = 0.32\,\mathrm{nm^{-1}} from the meridian; the first maximum of J1(x)J_1(x) occurs at x=1.84x = 1.84. ((a)) Find the helical pitch PP. ((b)) Find the axial rise per subunit hh. ((c)) Find the number of subunits per turn. ((d)) Find the helix radius rr, using r=x/(2πqr)r = x/(2\pi q_r) with x=1.84x = 1.84.

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