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Nuclear Magnetic Resonance Spectrometry Chap 19. Absorption in CW Experiments. Energy of precessing particle E = - μ z B o = - μ B o cos θ When an RF photon is absorbed by a nucleus, θ must change direction ∴ magnetic moment μ z “flips”

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## Nuclear Magnetic Resonance Spectrometry Chap 19

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**Absorption in CW Experiments**• Energy of precessing particle • E = -μz Bo = -μBo cos θ • When an RF photon is absorbed by a nucleus, • θ must change direction • ∴magnetic moment μz “flips” • For μz to flip, a B field must be applied ⊥ Bo in a • circular path in phase with precessing dipole • B is applied ⊥ Bo using circularly-polarized RF field**Fig 19-3 Model for the Absorption of Radiation**by a Precessing Particle μ’z**Fig 19-3 Model for the Absorption of Radiation**by a Precessing Particle When νRF = vo absorption and spin flip can occur**Fig 19-4 Equivalency of a Plane-polarized Beam to**Two (d, l) Circularly-polarized Beams • Result is vector sum that vibrates in a single plane • In instrument, RF oscillator coil is 90° to fixed Bo field • Only B rotating in precessional direction is absorbed**Classical Description of NMR**• Absorption Process • Relaxation Processes (to thermal equil.) • Spin-Lattice • Spin-Spin**Relaxation Processes (to thermal equilibrium)**• When absorption causes N1/2 = N-1/2 system is “saturated” • Fast decay is desirable • Probability of radiative decay (fluorescence) ∝ v3 • Therefore in RF region, non-radiative decay predominates**Bo field off:**α = βat random angles Magnetization is zero Bo field on: Spins precess around their cones at νLarmor αspins >βspins Net magnetization, M**Behavior of Magnetic Moments of Nuclei**Circularly-polarized radio frequency mag. field B1 is applied: When applied rf frequency coincides with νLarmor magnetic vector begins to rotate around B1**Spin-Lattice (Longitudinal) Relaxation**• Precessional cones representing • spin ½ angular momenta: • number βspins > number α spins • After time T1 : • Populations return to • Boltzmann distribution • Momenta become random • T1≡ spin-lattice relaxation time • Tends to broaden NMR lines**Spin-Spin (Transverse) Relaxation**• Occurs between 2 nuclei having • same precessional frequency • Loss of “phase coherence” • Orderly spins to disorderly spins • T2≡ spin-spin relaxation time • No net change in populations • Result is broadening**Fourier Transform NMR**• Nuclei placed in strong magnetic field, Bo • Nuclei precess around z-axis with momenta, M • Intense brief rf pulse (with B1) applied at 90° to M • Magnetic vector, M, rotates 90° into xy-plane • M relaxes back to z-axis: called free-induction decay • FID emits signal in time domain**Simple FID of a sample of spins with a single frequency**Fourier Transform NMR Spectrum**Vector Model of Angular Momentum**Fig. 19-2 55°

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