原子核在外磁场中的运动 P(z P(2 1 P Spin-122 in a magnetic field both i and l, are quantized the nuclear spin can only be orientated in( I+ 1) possible ways, with quantum number m ranging from-I to I(-1,-1+1,-1+2,.D) the most important nuclei in biology are the spin-1/2 isotopes H, 3C, 5N °F,and3P as spin-1/2 nuclei they can assume two states in a magnetic field, a(m 1/2)andβ(m=+1/2) THNMR YAN
原子核在外磁场中的运动 - in a magnetic field, both I and Iz are quantized - the nuclear spin can only be orientated in (2 I + 1) possible ways, with quantum number m ranging from -I to I (-I, -I+1, -I+2, … I) - the most important nuclei in biology are the spin-1/2 isotopes 1H, 13C, 15N, 19F , and31P - as spin-1/2 nuclei they can assume two states in a magnetic field, a (m = - 1/2) and b (m = + 1/2) THNMR YAN
磁矩的空间量子化 量子力学原则:外磁场中,自旋角动量与磁矩的取向是量 子化的 自旋角动量在z轴上的投影由磁量子数m决定,m有2H+1个 可能取值,即-,-/+1,,/-1, P=mh 核磁矩在z轴上的投影 u,=yP=ymh 磁矩和磁场的相互作用能 E=-μ·B0=-2B 原子核相邻能级间发生跃迁所需要的能量 THNMR AN △E=AmB0=hB
磁矩的空间量子化 量子力学原则：外磁场中，自旋角动量与磁矩的取向是量 子化的 自旋角动量在z轴上的投影由磁量子数m决定，m有2I+1个 可能取值，即 - I, -I + 1, … , I -1，I 核磁矩在z轴上的投影 磁矩和磁场的相互作用能 原子核相邻能级间发生跃迁所需要的能量 P z = m z = P z = m E B0 = −z B0 = −• E mB0 B0 = = THNMR YAN
Properties of Spin When placed in a magnetic field of strength Bo, a particle with a net spin can absorb a photon, of frequency v. The frequency V depends on the gyromagnetic ratio, y of the particle h=△E=YhB0 Memo: Vo=(/2 )x Bo y B THM For hydrogen, v=42. 5 8 MHZ/T AN
Properties of Spin When placed in a magnetic field of strength B0 , a particle with a net spin can absorb a photon, of frequency . The frequency depends on the gyromagnetic ratio, of the particle. 0 = (/2) B0 For hydrogen, = 42.58 MHz / T. 0 B0 Memo: = THNMR YAN hv E B0 = =
Nuclei with Spin Nuclei Unpaired Unpaired Net Spin Protons Neutrons (MHz/T) HHP 0 1/2 42.58 6.54 31 2 №NF 111111 1/2 17.25 3/2 1.27 3.08 10.71 1/2 40.08 THNMR YAN
Nuclei with Spin Nuclei Unpaired Protons Unpaired Neutrons Net Spin (MHz/T) 1 H 1 0 1/2 42.58 2 H 1 1 1 6.54 31P 0 1 1/2 17.25 23Na 2 1 3/2 11.27 14N 1 1 1 3.08 13C 0 1 1/2 10.71 19F 0 1 1/2 40.08 THNMR YAN
The larmor frequency can be understood as the recession frequency of the spins about the axis of the magnetic field B THNMR YAN
The Larmor frequency can be understood as the precession frequency of the spins about the axis of the magnetic field B0 THNMR YAN