Nuclear Magnetic Resonance Spectroscopy: Theory and Applications
473
Table 1 Nuclear spin quantum numbers (I) with their representative examples
No. of protons No. of neutrons Atomic mass Spin quantum
number (I)
Examples
Case-a Even
Even
Even
0
12 C, 16 O, 32 S
Case-b Odd
Even
Odd
½
1 H, 15 N, 19 F, 31 P
Even
Odd
Odd
½
13 C
Odd
Even
Odd
3/2
11 B, 79 Br, 35 Cl
Even
Odd
Odd
5/2
127 Te
Case-c Odd
Odd
Even
1
2 H, 14 N
(ii) Nuclei which have number of neutrons plus the number of protons are odd,
exhibit half integral quantum number (1/2, 3/2, 5/2 etc.). These nuclei behave
like spinning spheres.
(iii) Nuclei in which number of neutrons and the number of protons both are
odd, then the nucleus has an integral spin (I = 1, 2, 3 etc.) and exhibit
non-symmetrical charge distribution.
Number of orientations adopted by spin-active nucleus in strong magnetic field
can be described by equation (2I + 1). Nuclei with spin-half (for e.g.
1 H,
13 C and
19 F) can have only two orientations and called as ‘quadrupole nuclei’. The magnetic
moment of nucleus (μ) having spin quantum number (I) can be given by equation,
μ = γ × I
where, γ is a constant called as ‘gyromagnetic ratio’ of the nucleus.
The nucleus with spin quantum number I = 1/2 will be separated into two energy
levels having spin angular momentum with I = +1/2 and −1/2 i.e. parallel and
perpendicular to the direction of applied magnetic field. That means spin quantum
number I has two possible values—I = +1/2(h/2π) and −1/2(h/2π) where h is
Planck’s constant.
In that case, energies E 1 and E 2 for the two states can be calculated as,
E 1 = +B o μ = +B o γ(1/2)(h/2π)
E 2 = −B o μ = −B o γ(1/2)(h/2π)
E = E 1 − E 2 = +B o μ − (−B o μ)
E = +B o γ(1/2)(h/2π)−{−B o γ(1/2)(h/2π)}
E = B o γ(h/2π)
When electromagnetic wave of radiofrequency radiation having frequency υ is
applied to the nucleus, the nuclei of lower energy state absorb energy and promoted
to higher energy state that means absorption of energy changes magnetic moment
parallel to anti-parallel state.
473
Table 1 Nuclear spin quantum numbers (I) with their representative examples
No. of protons No. of neutrons Atomic mass Spin quantum
number (I)
Examples
Case-a Even
Even
Even
0
12 C, 16 O, 32 S
Case-b Odd
Even
Odd
½
1 H, 15 N, 19 F, 31 P
Even
Odd
Odd
½
13 C
Odd
Even
Odd
3/2
11 B, 79 Br, 35 Cl
Even
Odd
Odd
5/2
127 Te
Case-c Odd
Odd
Even
1
2 H, 14 N
(ii) Nuclei which have number of neutrons plus the number of protons are odd,
exhibit half integral quantum number (1/2, 3/2, 5/2 etc.). These nuclei behave
like spinning spheres.
(iii) Nuclei in which number of neutrons and the number of protons both are
odd, then the nucleus has an integral spin (I = 1, 2, 3 etc.) and exhibit
non-symmetrical charge distribution.
Number of orientations adopted by spin-active nucleus in strong magnetic field
can be described by equation (2I + 1). Nuclei with spin-half (for e.g.
1 H,
13 C and
19 F) can have only two orientations and called as ‘quadrupole nuclei’. The magnetic
moment of nucleus (μ) having spin quantum number (I) can be given by equation,
μ = γ × I
where, γ is a constant called as ‘gyromagnetic ratio’ of the nucleus.
The nucleus with spin quantum number I = 1/2 will be separated into two energy
levels having spin angular momentum with I = +1/2 and −1/2 i.e. parallel and
perpendicular to the direction of applied magnetic field. That means spin quantum
number I has two possible values—I = +1/2(h/2π) and −1/2(h/2π) where h is
Planck’s constant.
In that case, energies E 1 and E 2 for the two states can be calculated as,
E 1 = +B o μ = +B o γ(1/2)(h/2π)
E 2 = −B o μ = −B o γ(1/2)(h/2π)
E = E 1 − E 2 = +B o μ − (−B o μ)
E = +B o γ(1/2)(h/2π)−{−B o γ(1/2)(h/2π)}
E = B o γ(h/2π)
When electromagnetic wave of radiofrequency radiation having frequency υ is
applied to the nucleus, the nuclei of lower energy state absorb energy and promoted
to higher energy state that means absorption of energy changes magnetic moment
parallel to anti-parallel state.