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 I eveneven0 oddoddinteger 1,2,3 … evenoddhalf integral 1/2, 3/2, 5/2… oddevenhalf 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)} 1/2 ħ 2. A component of angular momentum m I ħ on an arbitrary axis where m I =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 m I.  m I ħ

Nuclei in Magnetic Field In a magnetic field B (in z direction) there are 2I+1 orientations of nucleus with different energies. B 0 : magnetic field in z direction L : Larmor Frequency

Nuclei in Magnetic Field For I=1/2 nucleus : m I = 1/2 and – 1/2

Nuclei in Magnetic Field

Distribution 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

HoHo anti-parallel parallel Two spins All spins  Sum Bulk Magnetization excess facing down Nuclei in Magnetic Field

p ap 1. equilibrium EE p ap 3. non-equilibrium p ap 5. equilibrium h  E 4. release energy (detect) h  E H1H1 2. pump in energy Effect of a radio frequency

NMR Signals

Relaxation- Return to Equilibrium t z axisx,y plane t E -t/T 2 t 1-e -t/T 1 t Longitudinal Transverse Transverse always faster!