CHAPTER 13: MAGNETIC RESONANCE

CHAPTER 13: MAGNETIC RESONANCESandra Bintara Putra3225111265Nuclear Magnetic ResonanceNMR is the most powerful tool available for organic structure determination.Nuclear SpinA nucleus with an odd atomic number or an odd mass number has a nuclear spin.The spinning charged nucleus generates a magnetic field.

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Two Energy StatesThe magnetic fields of the spinning nuclei will align either with the external field, or against the field.

A photon with the right amount of energy can be absorbed and cause the spinning proton to flip.

E and Magnet StrengthEnergy difference is proportional to the magnetic field strength.E = h = h B0 2Gyromagnetic ratio, , is a constant for each nucleus (26,753 s-1gauss-1 for H).In a 14,092 gauss field, a 60 MHz photon is required to flip a proton.Low energy, radio frequency.Magnetic ShieldingIf all protons absorbed the same amount of energy in a given magnetic field, not much information could be obtained.But protons are surrounded by electrons that shield them from the external field.Circulating electrons create an induced magnetic field that opposes the external magnetic field.

NMR SignalsThe number of signals shows how many different kinds of protons are present.The location of the signals shows how shielded or deshielded the proton is.The intensity of the signal shows the number of protons of that type.Signal splitting shows the number of protons on adjacent atoms.Line WidthMagnetic field seen by a magnetic dipole 1 due to another dipole 2 is

nearest neighbor interaction dominant:

For protons 2A apart,

H2 OMotional Narrowing

Li7 NMRin metallic Lidiffusion ratehighlow rigid latticeMotion narrowed

= diffusion hopping timeEffect is more prominent in liquid, e.g., proton line in water is 105 the width of that in ice. (rotational motion) T2 ~ time for spin to dephase by 1 radian due local perturbation Bi .

After t = n (random walk) Average number of steps for a spin to dephase by 1 radian is

whereas

for a rigid lattice

since

H2O: ~10 10 s

Hyperfine Splitting

current loopHyperfine interaction : between nucl = I & eContact hyperfine interaction:when e is in L = 0 stateDirac: B ~ circulation of e with v = c,

L = 0 Bohr magneton

Current in loop =

Compton wavelength

field at loop center =

Probability of e overlaping the nucleus :

Average field seen by nucleus:

Contact hyperfine interaction:

High field: B B >> aS = I =

Number of hf splittings = (2I + 1) (2S+1)Selection rule for e:mS = 1mI = 0

Selection rule for nucl:mS = 0

intersellar H

Examples: Paramagnetic Point DefectsF centers in Alkali Halides ( negative ion vacancy with 1 excess e )

K39 , I = 3/2Vacancy surrounded by 6 K39 nuclei

Number of hf components: 2Imax +1 = 19Number of ways to arrange the 6 spins:( 2I + 1)6 = 46 = 4096Donor Atoms in SiliconP in Si (outer shell 3s23p3): 4es go diamagnetically into covalent bonding; 1e acts as paramagnetic center of S = 1/2.

motion narrowing due to rapid hoppingKnight ShiftKnight (metallic) shift:B0 required to achieve the same nuclear resonance for a given spin depends on whether it is embedded in a metal or an insulator.

For conduction electrons:

Knight shift :

aatom ametal for Li,| metal(0)|2 ~ 0.44|atom(0)|2