THEORY OF NUCLEAR MAGNETIC RESONANCE (NMR)

The nuclei only that's the nmr phenomenon are those for which they spin quantum number " I" greater than σ . The spin quantum number "I" is the associated with the atomic number and mass number of atomic nuclei as follows :

Mass number                   Atomic number

1) odd                                1) odd or even

2) even                               2) even

3) even                               3) odd

Spin quantum number (I)             Example :

1) 1/2, 3/2, 5/2.....                  1)¹H,¹³C,¹⁹F, ³¹P

2) 0..........                                2) ¹²C,¹⁶O

3) 1, 2, 3......                            3)²H

                             The nucleus of ¹H, this proton, has I= 1/2, whereas ¹²C and ¹⁶O have l = 0 and are therefore nonmagnetic. If  ¹⁶O, ¹²C had been magnetic, the nmr spectra of organic molecules would have been much more complex, other important magnetic nuclei that has been studied extensively by nmr are ¹¹B, ¹³C, ¹⁹F and  ³¹P.

                                 Under the influence of the external magnetic field is, a magnetic nucleus it can take up different orientation with respect to that field : the number of possible orientation is given by (2l +1), so that for nuclei with spin 1/2, only two orientation are allowed.  ¹⁴N and Deuterium have l =1 and so it can take up three orientation, and this nuclei don't simply posses magnetic dipoles, but rather posses " electric quadruples". The nuclei processing electric quadrupoles can interact both with electric and magnetic field gradients.

                  In applied magnetic field, magnetic nuclei like the proton precess at a frequency υ, which is the proportional to the strength of the applied field, The maximum exact frequency is given by

          V = μ βN B⁰    υαβ₀

                    hl

Where, B₀ =  strength of the applied field experienced by the proton

I = spin quantum number

h = planck's constant

μ = magnetic moment of the particular atomic nucleus,

βN = nuclear magneton constant

              Typically, approximate value for frequency υ are shown in the following table for selected value of field β₀, for common magnetic nuclei.

B₀/tesla    1.4T                2.1                      7.1

Nucleus        Precessional frequencies

¹H             60                     90                     300

²H            9.2                     13.0                 46.0

¹³C           15.1                   22.6                 75.5

                     Even with very largely magnetic fields, upto 7.1T, the energy difference is

  ∆E = hυ is very small, upto 300MHz. Because the difference is almost nearly equal, the population of protons in the two energy levels are at room temperature shown that the lower energy state has a nuclear population only about that 0.001 percent greater than that of the higher energy states. The relative population of the spin states will changes, if energy is supplied of the correct frequency to induced transitions downwards or upwards.

                                 Author :

                                 Jesu Nallathambi and selvaraj