Physical Chemistry , 1st ed.

particles most popular in our treatment of quantum mechanics: the electrons.

However, atoms also have nuclei, which have many of the same properties that

electrons have. In particular, many nuclei also have a total spin and a magnetic

dipole.

Although we recognize that nuclei are composed of individual nuclear par-

ticles (protons and neutrons), from our perspective it is simplest to think of a

nucleus as a single particle that has properties determined by all of the nuclear

particles together. A nucleus therefore has a certain total charge, which is typ-

ically denoted Z. A nucleus also has a total spin angular momentum, which in

the previous section was denoted I. The total spin angular momentum (“spin”)

of a nucleus is determined by the number and pairing of the individual nu-

clear particles (whose angular momenta interact using rules similar to those

that govern electrons, but they are not the same and will not be considered

here). For example, the hydrogen nucleus, a single proton, has a nuclear spin I

of^12 . A deuterium nucleus has a nuclear spin of 1, and a tritium nucleus has a

spin of^12 .^12 C has a nuclear spin of 0, and^13 C has a nuclear spin of^12 .The

metastable isotope^134 Cs, which is radioactive and has a half-life of 2.90 hours,

has an Iof 8, the largest of any atomic nucleus.

Nuclear spins behave like electron spins in that there is a quantized value

for the total spin, and a quantized value for the zcomponent of the total spin,

symbolized by MI. (We used this idea in the previous section.) For our pur-

poses, it is important to recognize that, just like one or more electrons in an

atom, a nucleus having a nonzero spin has a magnetic dipole associated with

it. A nuclear magnetic dipolecan be defined, similarly to the electron’s magnetic

dipole. Starting with the smallest nucleus, that of the hydrogen atom, we have

the nuclear magnetic dipole of the proton, which is given as

pgp

2 m

e

p

Ip (16.18)

which, when multiplied by / , becomes analogous to equation 16.10 for

electrons. Here,Ipis the total spin angular momentum of the proton, which

follows the normal quantum-mechanical rules for total angular momentum:

I^2 pI(I 1) 

2 , so IpI(I 1 ). Equation 16.18 also allows us to define

an analogous magneton called the nuclear magnetonN:

N

2

e

m

p

 (16.19)

where eis the charge on the proton ( 1.602  10 ^19 C) and mpis the mass

of the proton (1.673  10 ^27 kg). This nuclear magneton has a value of about

5.051  10 ^27 J/T and is used to determine energy changes for all nuclei, not

just the proton. The gpin equation 16.18 is the gfactor for the proton, and (for

reasons we won’t go into) has a value of 5.586. Other nuclei have their own

characteristic values for gN. The nuclear magnetic moment of a single proton

is about 2.443  10 ^26 J/T.

Example 16.9

Compare the relative magnitudes of the electron’s magnetic moment and the

proton’s magnetic moment. Why are they different?

Solution

The magnetic moment of the hydrogen atom nucleus, a proton, is 2.443 

10 ^26 J/T. The electronic magnetic moment is found by using equation 16.10:

572 CHAPTER 16 Introduction to Magnetic Spectroscopy