Concise Physical Chemistry

c18 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

NUCLEAR MAGNETIC RESONANCE (NMR) 297

1 A in length should have ̊

μ=qr=

(

4. 80 × 10 −^10

)

×

(

1. 00 × 10 −^8

)

= 4. 80 × 10 −^18 esu cm

This is called a debye, D. In SI units of coulomb meters, 1 D= 3. 338 × 10 −^30 Cm.

We have just assumed that the negative charge is at one end of the molecule and

the positive charge is at the other, that is, that the bond is completely ionic. Molecules

are not completely ionic and many of them are not completely covalent either. The

intermediate case is a compromise called apolar molecule, which has some charge

separation but which is not totally ionic. One can obtain a numerical parameter telling

where this compromise lies by computing the dipole moment expected for a perfectly

ionic bond and comparing it with the measured moment. The ratio of the measured

moment to the moment calculated assuming complete charge separation leads to the

% ionic characterof the actual molecule.

18.8 NUCLEAR MAGNETIC RESONANCE (NMR)

Some atoms, including hydrogen H, have the property of nuclear spin, which produces

a small magnetic field. In the absence of an external field, the spin magnetic fields

of nuclei are randomly oriented; but in a magnetic field, they orient themselves with

or against the external field according to their spin quantum numbers,±^12 in the

case of the proton H. One orientation is energetically favorable, whereas the opposite

orientation is unfavorable. Twofold energy splitting occurs:

No Field Field

As usual, the lower energy level is more populous but the interaction between the

spin field and the external field is weak, so energy splitting is very small (of the order

of a few thousandths of a calorie per mole). A Boltzmann calculation for this minute

energy separation shows that the lower level has a population that is only a few nuclei

per hundred thousand greater than that of the upper level.

In principle, NMR is the same as other kinds of spectroscopy, but important tech-

nical differences exist. In absorption spectroscopy, incident electromagnetic radiation

is varied until a resonant frequency coincides with the energy-level separation nec-

essary to promote the system from a lower quantum state to a higher state. Emission

spectroscopy, which is preferred for some purposes, involves the reverse process,

emission of radiation occasioned by the fall of particles from a higher state to a lower

state. If both upper and lower energy states are appreciably populated, electromag-

netic radiation can induce both absorption and emission of energy.