NMR Spectroscopy

Part I. Origin of NMR

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

p

: magnetic moment

p: angular momentum

: magnetogyric ratio

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 Ieven even 0

odd odd integer 1,2,3…

even odd half integral 1/2, 3/2, 5/2

…

odd even half integral 1/2, 3/2, 5/2

…

Nuclei in Magnetic Field Properties of nucleus with spin

quantum number I

1. An angular momentum of magnitude {I(I+1)}1/2ħ

2. A component of angular momentum mIħ on an arbitrary axis where mI=I, I-1, … -I (magnetic quantum number)

3. When I>0, a magnetic moment with a constant magnitude and an orientation that is determined by the value of mI. mI ħ

Nuclei in Magnetic Field In a magnetic field B (in z direction) there are 2I+1

orientations of nucleus with different energies.

LIIm hvmmBBEI

00 h

B0: magnetic field in z direction

L: Larmor Frequency 2/Bv

Nuclei in Magnetic Field

For I=1/2 nucleus : mI = 1/2 and –1/2

0

002/1

002/1

2

2

BE

BmBE

BmBE

I

I

h

hh

hh

Nuclei in Magnetic Field

Nuclei in Magnetic Field

Nuclei in Magnetic Field

Nuclei in Magnetic Field

kT

B

kT

B

kT

E

N

N00

21

21

1exp)exp(

Nuclei in Magnetic FieldDistribution between two states

Nuclei in Magnetic Field

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)

Magnetizaton

Nuclei in Magnetic Field

Ho

anti-parallel

parallel

Two spins All spins Sum

Bulk Magnetizationexcess

facingdown

Nuclei in Magnetic Field

p

ap

1. equilibrium

E

p

ap 3. non-equilibrium

p

ap5. equilibrium

hE 4. release energy (detect)

hEH1

2. pump in energy

Effect of a radio frequency

Effect of a radio frequency

Effect of a radio frequency

1Ba

NMR Signals

Relaxation- Return to EquilibriumRelaxation- Return to Equilibrium

t

z axisx,y plane

0

1

2

t

0

1

2

8 8

E-t/T2

t

1-e-t/T1

t

LongitudinalTransverse

Transverse always faster!