Transcript 0_2_SA_LarmorPrecession

Spin Precession Animation “DEMO”
The Nucleus would
continue to precess; only
as long as the Magnetic
Field is on - - - - - - - -
- ->
Precession Starts
on application of
Magnetic Field
Animation in this
slide only one cycle
of the Larmor
precession
MAGNETIC
FIELD
μXH
SPIN
Iħ
MAGNETIC
MOMENT
Nuclear Spin
Electron and the Proton
Angular momentum &
Angular momentum &
Magnetic moment
along mutually
opposite direction
Magnetic moment
along the same
direction
Proton
Electron
“+ “ charge
“-” charge
The magnetic moment and
angular momentum are related by
a constant characteristic of the
subatomic particle.
This is the gyro magnetic ratio “γ”
For proton the “γ” is
positive and for the
electron “γ” is negative.
Since electron is much
lighter than proton, the
electron “γ” is 663 times
larger than that of proton.
A Thumb rule to work out Electron Spin Resonance Frequency [and
the corresponding Proton NMR frequency] is as follows:
since hν=gβH is the relation governing resonance condition, by
knowing the relevant constants from available data tables, it should
be verified that the following equation closely approximates the
resonance frequency-field criterion for ESR.
1 Gauss = 2.8 MHz for a free electron spin with g=2
For proton NMR
1 Gauss = 4.2 KHz
Therefore if one can detect the oscillator levels using an oscillatordetector, and , if the frequencies of the oscillations are in the range
of 8-32 MHz, then using the above equation the corresponding
1.9
resonance field can be calculated. 2.9 – 11.5 Gauss for ESR.
Further a simple Helmholtz coil can be designed to obtain these
Magnetic Field Strengths by providing a suitably designed current
sources which may be available even commercially.
– 7.6
K Gauss
Then a Block Diagram of the type shown in the next slide can be
appropriate for constructing and assembling a esr detection system.
for PMR
The Larmor precession
frequency depends on the
strength of external field
hν=gβH
If a rotating magnetic field of
relatively small magnitude is
present in the perpendicular
plane at frequency ν , then the
resonance occurs and the spin
undergoes a flipping transition to
another orientation.
For proton spin of
½, there are two
allowed
orientations so that
the component
along z-axis is
either +1/2 or -1/2
+1/2 ħ
Lower
energy
-1/2 ħ
Photon energy absorbed;
transition occurs
Radiation
+1/2 ħ
Induced Transition or stimulaed transition
-1/2 ħ
Upper
energy
random
No external magnetic field. The
energy levels are degenerate
-1/2
+1/2
The ensemble of spins,
have equally distributed
population between the two
levels for the spin ½ protons
No net magnetization
On the application of field…..
Splitting is instantaneous & population
redistribution requires more time called the
relaxation time
-1/2
No radiations
are present
-1/2
+1/2
Not stimulated
transitions: but
spontaneous
relaxation transitions
Magnetic field
+1/2
Degeneracy
removed/Energy levels split
Thermal equilibrium
Boltzmann distribution
Net magnetization