Physical Chemistry , 1st ed.

where Qis the total charge passing by a point per second. The area of a circu-

lar orbit is r^2. Combining the above equation with equation 16.2, one finds

that the magnetic dipole of this particle is



2

Q



v

r

r^2 

Q

2

vr

 (16.4)

Remember that the definition of the angular momentum Lis Lmrv, or in

our magnitude formalism,LLmvrmvr. Substituting, we find that



2

Q

m

L (16.5)

where we have now tied the magnetic dipole of a particle in a circular orbit to

its angular momentum. (By analogy, the vectors are also related:(Q/2m)L.)

For a single electron, the charge is e, which equals 1.602  10 ^19 C. In

this case, we have expressly included the minus sign on ebecause the electron is

considered negatively charged. For a single electron, equation 16.5 is written as



2 m

e

e

L

where meis the mass of an electron. Upon multiplying the last fraction by 1,

written as / ,we get



2 m

e

e^

L

The Bohr magneton,B, is defined as

B

2

e

m

e

 (16.6)

so that for an electron, the magnetic dipole can be written





BL (16.7)

Do not confuse the magnetic dipole,, for the symbol for the Bohr magne-

ton,B. The Bohr magneton has a value of about 9.274  10 ^24 J/T (joules

per tesla). It (or similarly defined constants) is a necessary constant for almost

all magnetic spectroscopies.

16.3 Zeeman Spectroscopy

One of the most straightforward and simple types of magnetic spectroscopy is

called Zeeman spectroscopy.Its existence was proposed in 1890 by the Dutch

physicist Hendrik Lorentz. If atoms were composed of electrical charges,

Lorentz said, these charges should be affected by a magnetic field and a change

would be noted in the atomic spectrum. In 1896 a student of Lorentz’s, Pieter

Zeeman, verified this prediction experimentally. For their work, Lorentz and

Zeeman shared a 1902 Nobel Prize.

A simple example of the Zeeman effect is as follows: a single, sharp line in

an atomic spectrum splits into three closely spaced, sharp lines when the sam-

ple is exposed to a magnetic field. The lines are extremely close: less than 1 cm^1

apart. However, the explanation for why the Zeeman effect occurs at all was

left for quantum mechanics to explain.

564 CHAPTER 16 Introduction to Magnetic Spectroscopy