NMR%20Spectroscopy

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NMR Spectroscopy

• Part I. Origin of NMR

2
Nuclei in Magnetic Field

• Nucleus rotate about an axis -- spin

Nucleus bears a charge, its spin gives rise to a
magnetic field . The resulting magnetic moment is
oriented along the axis of spin and is
proportional to angular momentum m g p

• magnetic moment
• p angular momentum
• g magnetogyric ratio

3
Nuclei in Magnetic Field

• Spin Quantum Number I
• a characteristic property of a nucleus. May be
  an integer or half integer

of protons of neutrons I even even 0 odd
odd integer 1,2,3 even even half
integral odd odd half integral
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Nuclei in Magnetic Field

• Properties of nucleus with spin quantum number I

1. An angular momentum of magnitude
I(I1)1/2h 2. A component of angular momentum
mIh on an arbitrary axis where mII, I-1, -I
(magnetic quantum number) 3. When Igt0, a magnetic
moment with a constant magnitude and an
orientation that is determined by the value of
mI. m g mI h
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Nuclei in Magnetic Field

• In a magnetic field B (in z direction) there are
  2I1 orientations of nucleus with different
  energies.

B0 magnetic field in z direction nL Larmor
Frequency
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Nuclei in Magnetic Field

• For I1/2 nucleus mI 1/2 and 1/2

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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
Distribution between two states
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
Magnetizaton
The difference in populations of the two states
can be considered as a surplus in the lower
energy state according to the Boltzmann
distribution A net magnetization of the sample is
stationary and aligned along the z axis (applied
field direction)
14
Nuclei in Magnetic Field
15
Effect of a radio frequency
16
Effect of a radio frequency
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Effect of a radio frequency
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NMR Signals
19
Relaxation- Return to Equilibrium
t
t
z axis
x,y plane
0
0
Longitudinal
Transverse
1
1
t
t
2
2
E-t/T2
1-e-t/T1
8
8
Transverse always faster!