the quantized states by Pauli’s exclusion principle (Fig. 3.5). And magnetic moment
is shown by μ ¼ À γ hS, by introducing gyromagnetic ratio γ, g-factor and Bohr
magneton β ¼
eh
2mc , and the magnetic moment replaced by μ ¼ À gβS. And
Hamiltonian¼gβH Á S z is obtained for along external magnetic field on z-axis.
Energy in parallel is shown by gβ À
1
2
À Á Á H and in antiparallel is shown bygβ Á À
1
2
À Á
ÁH (Fig. 3.6). Difference between these energy levels i.e. Zeeman energy is shown by
ΔE ¼ gβ
1
2
À Á
H À gβ À
1
2
À Á ¼ gβH, and electrons distribute these energy levels
according to Boltzmann distribution. More electrons distribute in lower level, and
radiated microwave ΔE to this system in resonance condition of hν ¼ gβH makes the
electrons in lower level to jump to upper level by absorbing the energy. And
simultaneously energy transfer to lower level occurs in relaxation process when
applied energy is smaller than certain energy. Difference of electron population is
maintained and ESR signal is observed stationary in this condition. Resonance
condition is determined by a tensor, g-factor. Value of g-factor for free electron is
N
S
Anti-paralel Paralel
External magnetic field
S N
N S
Fig. 3.5 Quantization of spins by external magnetic field
Quantum number of electron spin is 1/2 and quantized to anti-parallel or parallel
Electron spin is splitted to different energy levels of parallel (À1/2) and anti-parallel (1/2) by
Zeeman effect when external magnetic field is applied
Without magnetic field
With external magnetic field
Anti-parallel
Parallel
m=+1/2
m=-1/2
g e m B B 0
α
b
Fig. 3.6 Split of energy level of spin by external magnetic field
Electron spin is splitted to different energy levels of parallel (À1/2) and anti-parallel (1/2) by
Zeeman effect when external magnetic field is applied
3.6 Magnetic Resonance
35
is shown by μ ¼ À γ hS, by introducing gyromagnetic ratio γ, g-factor and Bohr
magneton β ¼
eh
2mc , and the magnetic moment replaced by μ ¼ À gβS. And
Hamiltonian¼gβH Á S z is obtained for along external magnetic field on z-axis.
Energy in parallel is shown by gβ À
1
2
À Á Á H and in antiparallel is shown bygβ Á À
1
2
À Á
ÁH (Fig. 3.6). Difference between these energy levels i.e. Zeeman energy is shown by
ΔE ¼ gβ
1
2
À Á
H À gβ À
1
2
À Á ¼ gβH, and electrons distribute these energy levels
according to Boltzmann distribution. More electrons distribute in lower level, and
radiated microwave ΔE to this system in resonance condition of hν ¼ gβH makes the
electrons in lower level to jump to upper level by absorbing the energy. And
simultaneously energy transfer to lower level occurs in relaxation process when
applied energy is smaller than certain energy. Difference of electron population is
maintained and ESR signal is observed stationary in this condition. Resonance
condition is determined by a tensor, g-factor. Value of g-factor for free electron is
N
S
Anti-paralel Paralel
External magnetic field
S N
N S
Fig. 3.5 Quantization of spins by external magnetic field
Quantum number of electron spin is 1/2 and quantized to anti-parallel or parallel
Electron spin is splitted to different energy levels of parallel (À1/2) and anti-parallel (1/2) by
Zeeman effect when external magnetic field is applied
Without magnetic field
With external magnetic field
Anti-parallel
Parallel
m=+1/2
m=-1/2
g e m B B 0
α
b
Fig. 3.6 Split of energy level of spin by external magnetic field
Electron spin is splitted to different energy levels of parallel (À1/2) and anti-parallel (1/2) by
Zeeman effect when external magnetic field is applied
3.6 Magnetic Resonance
35