20-Bio-B10 Biomechanical Device Design & Human Factors · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2017 — 04-Bio-B10 Analytical Biochemistry. Three hours, closed book, any non-communicating Casio/Sharp calculator. Six questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All six are solved here, because this set is a study resource rather than an examination script. The paper is essay/descriptive throughout, with two embedded PCR copy-number sub-questions (Q2b, Q2c) that carry numeric content.
Reference texts (the books a candidate should have reviewed for this subject):
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
First, the sample is placed in a strong, static, homogeneous magnetic field, B0. NMR-active nuclei (non-zero nuclear spin, e.g., 1H) possess a magnetic moment that aligns either with or against B0; the with-field (lower-energy) orientation is very slightly more populated (a small Boltzmann excess), producing a small net bulk magnetization along B0. Second, a short radiofrequency (RF) pulse, tuned to the nuclei's resonant (Larmor) frequency and applied perpendicular to B0, tips this net magnetization away from alignment with B0 and into the transverse plane (excitation). Third, once the pulse ends, the magnetization precesses in the transverse plane and relaxes back toward equilibrium (governed by the spin–lattice, T1, and spin–spin, T2, relaxation times), inducing a decaying, oscillating voltage in a detection coil — the free induction decay (FID), a time-domain signal containing every resonant frequency in the sample superimposed. Fourth, that FID is Fourier transformed from the time domain into the frequency domain, converting the composite decaying oscillation into a conventional NMR spectrum: a series of peaks at the chemical shifts (resonant frequencies, referenced in ppm) characteristic of each nucleus's local chemical/electronic environment.
The proton (1H) combines two properties that make it the most NMR-sensitive nucleus in routine use: it has essentially 100% natural isotopic abundance (virtually every hydrogen atom in a sample is the NMR-active 1H isotope), and it has the highest gyromagnetic ratio of any commonly encountered stable nucleus, which directly sets both its resonant (Larmor) frequency and its intrinsic sensitivity (signal strength scales with the cube of the gyromagnetic ratio for a fixed field). As a spin-½ nucleus, 1H also gives sharp, simple resonances free of the quadrupolar line-broadening seen for higher-spin nuclei. Combined with hydrogen's near-ubiquity in organic and biological molecules, these properties make 1H-NMR far more sensitive and practical than, for example, 13C (~1.1% natural abundance, lower gyromagnetic ratio) or 15N (very low abundance and sensitivity) — which is why 1H-NMR is the default, routine first experiment for structural elucidation.
Raising B0 improves NMR performance in two linked ways. First, chemical-shift dispersion: because chemical shift is measured on a relative (ppm) scale but the underlying resonant frequency is proportional to B0, a higher field spreads the same set of chemically shifted peaks further apart in absolute frequency (Hz), reducing peak overlap and resolving multiplets/closely spaced signals that would be unresolved at lower field. Second, sensitivity: the Boltzmann population difference between the aligned/anti-aligned spin states — and hence the net magnetization and the induced signal — grows with B0, so higher-field instruments deliver better signal-to-noise for a given sample amount and acquisition time (or allow smaller samples/shorter experiments for the same signal quality). Together, higher field means both better resolution and better sensitivity, at the cost of a larger, more expensive superconducting magnet system.
There is no hard physical floor — NMR resonance can in principle be observed at any nonzero field, and specialized "ultra-low-field" and "Earth's-field" NMR techniques have demonstrated detectable signals using nothing but the ambient geomagnetic field (on the order of 25–65 µT, roughly 0.5 Gauss), typically by combining long averaging times with sensitive SQUID magnetometers or hyperpolarization of the sample to compensate for the vanishingly small Boltzmann polarization at such a weak field. For routine, practical structural NMR spectroscopy, however, the achievable signal-to-noise and chemical-shift dispersion at such low fields are far too poor within a reasonable experiment time using ordinary thermally polarized samples and inductive detection coils; conventional benchtop and high-resolution NMR spectrometers therefore use permanent or superconducting magnets in the roughly 1–21+ Tesla range (corresponding to ~40–900+ MHz proton Larmor frequency), because usable sensitivity within minutes-to-hours of acquisition only becomes practical once the field is several orders of magnitude above the Earth's ambient field.
