16.2 Magnetic Fields and Dipoles,
and Electric Charges
16.1.What is the difference between a magnetic field vector
and a magnetic dipole vector?
16.2.Assuming that you are surrounded by six electrical wires
right now, each 2.00 meters away and that each one is carry-
ing 10 amps of charge in the same direction, what magnetic
field are you exposed to?
16.3. (a)If the electron were to have a positive charge, what
would be the difference in the magnitude calculated in
Example 16.2b for the magnetic dipole caused by an electron
in the hydrogen atom?
(b)Positroniumis very similar to a hydrogen atom except that
instead of a proton in the nucleus, there is a positron. (This
short-lived “element” can be made in the laboratory.) On the
basis of your answer to part a, what is the overall magnetic di-
pole caused by the two particles in mutual orbit about each
other?
16.4.Show that 1 tesla is equal to 1 J/(m^2 amp).
16.5.Verify the value and units of the Bohr magneton, B.
16.3 Zeeman Spectroscopy
16.6.Draw and label the allowed electronic transitions for a
(^1) S → (^1) P transition with and without a magnetic field. How do
the total number of allowed transitions differ?
16.7. (a)For the above^1 S →^1 P transition, calculate Ein the
transition energies for each individual transition when a sam-
ple is exposed to a magnetic field of 2.35 T. (b) Repeat the
calculation, but now for a^1 P →^1 D transition.
16.8.What magnetic field is needed to obtain a Evalue of
1.0 cm^1 between the highest and lowest levels of a^1 F state?
16.9.Calculate the maximum splitting of the^2 P3/2state of
the hydrogen atom due to Earth’s magnetic field, which you
can take as having a value of 0.6 gauss.
16.10.How many (a)individual transitions and (b)unique
spectral lines (that is, lines having a different energy) are al-
lowed for a^1 D →^1 P transition? (See exercise 16.7b.)
16.11.Calculate the Landé gfactor for a^5 D 4 state of the Fe
atom using both equations 16.12 and 16.13 and determine
the deviation introduced by approximating ge1.
16.12. (a) Calculate the E values experienced by the
ground-state energy levels when an atom of V is exposed to a
magnetic field of 5.57 103 G. Vanadium has an^4 F3/2ground
state.
16.4 ESR Spectroscopy
16.13.What are the energies in J/photon for the microwave
radiation frequencies used in ESR spectroscopy?
16.14.What magnetic field strengths are necessary to achieve
resonance for each of the microwave frequencies used in ESR
spectroscopy?
16.15.How many ESR signals would be expected from the
amine radical, NH 2 ?
16.16.How many ESR signals would be expected from the
cyclopentadienyl radical, C 5 H 5 ?
16.17.How many ESR signals would be expected from the
cycloheptatrienyl radical, C 7 H 7 ?
16.18.What magnetic field strength is necessary to achieve
resonance between the two spin states of an electron on a
compound where the difference in the energy levels is
7.204 10 ^24 J? Assume a gevalue of 2.0023.
16.19.What is the wavenumber of the microwave radiation
absorbed by an unpaired electron in a magnetic field of
3476 gauss that has a gevalue of 2.0058?
16.20.Nitrogen makes oxide compounds of varying stoi-
chiometry, including NO, NO 2 , N 2 O 4 , and N 2 O 5. Predict which
of these molecules will be ESR-active in their un-ionized, mo-
lecular form.
16.21.An ESR spectrum of an unknown radical is split into
six lines. Which of the following atoms could be in the radi-
cal? (a)^42 K (b)^35 Cl (c)^37 Cl (d)^67 Zn (e)^47 Ti (f)^32 S (Hint:
A table of nuclear spins is necessary to answer this question.
Such a table is in Appendix 5 of this text.
16.22.The hyperfine coupling constant afor deuterium, D
(which is^2 H), is 78 gauss. Predict the ESR spectrum of the ND 2
radical at a magnetic field of 3482 gauss.
16.5 NMR Spectroscopy
16.23.Do the NMR transitions from MI^12 to MI ^12 ap-
pear at the same wavelengths or different wavelengths from
the MI ^12 to MI ^32 transition of the same nucleus? Justify
your answer mathematically.
16.24.Which of the following nuclei will have an NMR spec-
trum? (a)^2 H (b)^14 C (c)^16 O (d)^19 F (e)^28 Si (f)^31 P
(g)^55 Mn (h)^238 U (Hint:Again, a table of nuclear spins is nec-
essary for this question. See Appendix 5 for the data you need.)
584 Exercises for Chapter 16
EXERCISES FOR CHAPTER 16