Physical Chemistry Third Edition

1010 24 Magnetic Resonance Spectroscopy

The values that thezcomponents of the nuclear spin can take on are

IzhM ̄ I (MII,I−1,...,−I+1,−I) (24.2-17)

For a proton, the quantum numberMIcan equal 1/2or− 1 /2. For a deuterium (^2 H)

nucleusMIcan equal 1, 0 or−1, and so on. Thezcomponent of the magnetic dipole

can take on values

μzgNβNMI (MII,I−1,...,−I+1,−I) (24.2-18)

If a nucleus is placed in a magnetic fieldBzin thezdirection the magnetic energy is

proportional toBz:

Emag−μzBz−gNβNMIBz−γhM ̄ IBz (24.2-19)

A proton could be in either of two energy states withMI± 1 /2, as could a^13 C

nucleus. A deuterium nucleus could be in any of three energy states withMI1, 0, or

−1, and so on.

PROBLEMS

Section 24.2: Electronic and Nuclear Magnetic Dipoles

24.4 It is not known if the electron has any internal structure, but
string theoryhypothesizes that all “fundamental” particles
consist of vibrations in tiny strings about 10−^35 m in size.
a.Assume that a charge equal to the charge on an electron
is moving in a circular orbit 1. 00 × 10 −^35 m in radius.
Calculate the speed of the charge if it produces a
magnetic dipole equal to that of an electron. Compare
this hypothetical speed with the speed of light.
b.Find the energy of a particle with mass equal to that of
an electron with a de Broglie wavelength equal to the
circumference of a circle 1. 00 × 10 −^35 m in radius.
Compare this energy with the rest-mass energy of an
electron.

24.5 Repeat the calculation of the previous problem for a charge
equal to the charge on a proton moving in a circular orbit

1. 00 × 10 −^15 m in radius (roughly equal to a typical
   nuclear size).

24.6Assume that the earth’s magnetic field at some location is

equal to 0.500 gauss (5. 00 × 10 −^5 T).

a.Find the difference in the energy of the two spin states

of an electron in this magnetic field.

b. Find the frequency and the wavelength of a photon with

the energy of part a.

24.7Assume that the earth’s magnetic field at some location is

equal to 0.500 gauss (5. 00 × 10 −^5 T).

a.Find the difference in the energy of the two spin states

of a proton in this magnetic field.

b. Find the frequency and the wavelength of a photon with

the energy of part a.

24.8 a.Find the value of the magnetogyric ratio for^7 Li nuclei.

b.Find the value of the magnetogyric ratio for^13 C nuclei.

c.Find the value of the magnetogyric ratio for^17 O nuclei.

24.3 Electron Spin Resonance Spectroscopy

From Eq. (24.2-6) the energy of an electron in a magnetic fieldBzis

EmaggβeBzms−±

gβeBz

2

(24.3-1)