Concise Physical Chemistry

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

PROBLEMS AND EXAMPLES 299

Intensity

FIGURE 18.9 Schematic NMR spectrum of ethanol, CH 3 CH 2 OH. The CH 3 peak on the

right is split into a triplet because of the two neighboring protons on CH 2.

nuclei to relax to their equilibrium states after being pulsed by frequency excitation

leads to powerful diagnostic methods known asmagnetic resonance imaging(MRI).

18.9 ELECTRON SPIN RESONANCE

Electrons also have the property of spin and, if spins are unpaired, as in free radi-

cals, electron spin gives rise to an electron spin resonance ESR spectrum, which is

analogous to NMR. ESR spectra are useful in the characterization of free radicals,

in their detection as reactive intermediates, and in specifying the electron probability

distribution within the radical. Free radicals have been implicated in carcinogenesis

and in aging, but other free radicals appear to act as sweepers reacting with destructive

species before they can harm a host organism.

PROBLEMS AND EXAMPLES

Example 18.1 The Bond Strength and Bond Length of Carbon Monoxide

Experimental results are that a low-resolution peak can be found for^12 C^16 O centered

around 2142 cm−^1 , which separates at high resolution to show a peak separation of

3.8 cm−^1. Find the bond length and the force constant. The superscripted 12 and

16 indicate that these data are for the predominant isotopes of C and O. Other, far

smaller peaks can be found for the other isotopes. Because this is the experimental

information for^12 C^16 O, the isotopic weights can be treated as integers.

Solution 18.1

1. One needs the reduced mass for both calculations. For^12 C^16 O the reduced
   mass is

μ=

12. 00 ( 16. 00 )

12. 00 + 16. 00

1. 661 × 10 −^27 = 1. 139 × 10 −^26 kg