Download PS10_Wk12_122 S17

Chemistry 122
Prof. Mines
PS10 Sheet (Wk12)
Notes or Comments:
Course documents can be downloaded from: http://www.oakton.edu/~gmines/CHM122
For data (half-life, decay types, binding energies, etc.) on just about all known isotopes/nuclides go to:
http://atom.kaeri.re.kr/
Assignments:
Read and study Sections 20.1-20.3 (focusing on 20.3), 20.4 (read “Magic Numbers” only for interest—do
not memorize these!), 20.6 (note that Tro does not use the term “Activity” for “rate of decay”—he just uses
“rate”), 20.7-20.8 (only scanning 20.7 but focusing on 20.8)*, this week while working on the problem set.
Scan 20.9 only to make sure you know what fusion “is”, generally speaking. Sections 20.5, and 20.1020.12 may be scanned for interest, but you are not responsible for any factual information within.
*Notes: on p. 961, Tro makes what I believe to be an error in stating “in order to compare the binding energy of one nucleus to that of
another, we calculate the binding energy per nucleon, …”. I believe the words “binding energy” should be replaced with the words
“thermodynamic stability” to make this statement correct. On p. 962, he also errs in not qualifying that nuclear fission is only “a
highly exothermic process” for nulclides with A > 60 (well above 60, really), and that “Both fission and fusion emit large amounts of
energy…” without qualifying that it is only the fusion of small nuclides and the fission of large nuclides that release energy—the
fusion of large nuclides and the fission of small ones would be endothermic! This is very important!
Problem Set #10 (due as noted on syllabus)
All 12 problems for this set are “M” problems. I have added “cross references” to similar problems in Tro to help
you use the text more effectively. I may also incorporate some of those problems into the PS10 Mastering set.
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Nucleon: a particle in the nucleus (either a proton or a neutron)
Atomic Number (Z): the number of protons in the nucleus. Defines “who
you are” if you are a nucleus.
Mass Number (A): total number of protons AND neutrons (p + n) (i.e., the
total number of nucleons) in a nucleus.
Note: This integer is not a mass, but a “number” (integer). However, it is called
a mass number because the atomic mass (in units of amu) will be very close to
the value of the mass number. This is true because protons and neutrons each
have a mass of approximately one amu.
Nuclide
He-5
Be-10
N-15
Mg-30
Ni-60
Cd-120
Cm-240
Mass #
5
10
15
30
60
120
240
Eb (MeV)
24.41
64.98
115.49
241.6
526.8
1015
1810
Eb/nucleon
6.50
7.70
8.05
7.54
Isotopes of an Element have the same number of protons (otherwise they wouldn’t be of the same element!) in their atoms’
nuclei, but a different number of neutrons. This means that the mass numbers will differ as well.
77
Complete Symbol of an isotope: Z X , where X is the abbreviation for the element. E.g., 35 Br represents the isotope of Br
in which each atom’s nucleus contains 35 protons and 42 neutrons (77 nucleons in total). It will have a mass of near 77
amus (but not ”exactly” 77 amus!)
A
Nuclide: A nucleus that has a specified number of neutrons (and protons, obviously) in it. In other words, a nucleus of an
atom of a specific isotope. E.g., one type of carbon atom is the version that has 7 neutrons. This isotope of C has the
symbol 13C. A nuclide with 6 p’s and 7’s would also have the symbol 13C.
-----------------------------------------------------------------------------------------------------------------------M1. Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in
parentheses, except for electron capture, where an electron is a reactant.)
(a) 68Ga (electron capture);
(b) 62Cu (positron);
(c) 212Fr ();
(d) 129Sb ()
M2. In each of the following nuclear reactions, supply the missing particle.
(a) 73Ga →
73Ge
+ ____
(b)
192Pt
→
188Os
+ ___
(c)
205Bi
→
205Pb
+ ____
(d)
241Cm
+ ____ →
241Am
(e) 137Ba → 137Ba + ____
See Tro Q’s 20.35 & 20.36 (p. 973)
See Tro Examples 20.1 (p. 942) and 20.2
(p.944), and Q’s 20.31 & 20.32 (p. 973)
Chemistry 122
Prof. Mines
M3. (a) What is the zone/valley of stability?
See Tro Section 20.4 (pp 946-947)
(b) Stable light nuclides have about equal numbers of neutrons and protons. What happens to the neutron–to-proton ratio
for stable nuclides as the number of protons increases?
(c) Nuclides that are not already in the zone of stability undergo radioactive processes to [ultimately] get to the zone of
stability. If a nuclide has too many neutrons, which process(es) can the nuclide undergo to become more stable?
(d) Answer the same question (as in (c)) for a nuclide having too many protons.
M4. (a) The only stable isotope of fluorine is F-19. Predict possible modes of decay for F-21, F-18, and F-17.
(b) Also predict possible modes of decay for 210Po, and (c) 195Au.
See Tro Q’s 20.41 & 20.42 (p. 973)
M5. Complete the following nuclear reactions. NOTE: [All have been used to synthesize elements.]
(a) ____ 
4
2
He 
(b)
238
92
U 
(c)
249
98
Cf  ____ 
(d)
249
98
Cf
12
6

243
97
Bk 
1
0
n
See Tro Conceptual Connection 20.4 (p. 964)
C  ____  6 n
1
0
10
5
B 
260
105
Db  4 01 n
257
103
Lr  2 ____
M6. Radioactive copper-64 decays with a half-life of 12.8 days.
(a) What is the value of k in s-1?
For M6-M8, see Tro Examples 20.4 (p. 951), 20.5 (p. 953), and
20.6 (p. 954), and Q’s 20.45 through 20.56 (pp 273-4)
(b) A sample contains 28.0 mg 64Cu. How many decay events will be produced in the first second? (i.e., Calculate the
initial rate in decays per second!) Assume the atomic mass of 64Cu is 64.0 (amu).
(c) A chemist obtains a fresh sample of 64Cu and measures its radioactivity. She then determines that to do an experiment,
the radioactivity cannot fall below 25% of the initial measured value. How long does she have to do the experiment?
M7. Fresh rainwater or surface water contains enough tritium ( 31H ) to show 5.5 decay events per minute per 100. g of water.
Tritium has a half-life of 12.3 years. Pretend that the year is 2009 (rather than the current year). You are asked to
check a vintage wine that is claimed to have been produced in 1946. How many decay events per minute should you
expect to observe in 100. g of that wine if the claim is true? (Again, assume it is 2009 right now.)
M8. Assume a constant 14C/12C ratio of 13.6 counts (same as “disintegrations”) per minute per gram of living matter. A
sample of petrified tree was found to give 1.2 counts per minute per gram. How old was the tree? (t1/2 of 14C is 5730
years.)
M9. A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases 4 x 109
J of energy when exploded. Using 2 x 1013 J/mol as the energy released by fission of 235U, (a) approximately what
mass of 235U undergoes fission in this atomic bomb? (b) Does the bomb have more mass or less mass after the
explosion? By how much (in mg)?
For M9 (b), see Tro 20.65 (p. 974)
M10. (a) What is meant by the terms “binding energy” and “mass defect”?
(b) Describe clearly in words how you could calculate the binding energy for a nuclide using the precise masses of a nuclide
as well as the mass of a (free) proton and a (free) neutron. Hint: write out the nuclear equation corresponding to the
binding energy.
M11. (a) What is the difference between fusion and fission? (define each)
(b) If the binding energy of Ar-40 is 343.8 MeV, what is the binding energy per nucleon?
(c) What is the difference between “binding energy” and “binding energy per nucleon”? Which one helps you predict
whether or not a nuclide will undergo fission or fusion to lower its energy?
(d) Do larger nuclides always have larger binding energies? Do larger nuclides always have larger binding energies per
nucleon?
(e) Of the nuclides in the table shown on the first page of this PS10 sheet, which one(s) are more thermodynamically
stable than Ar-40? [see part (b)] (Note: You may need to calculate some values omitted from that table.)
2
3
2
3
M12. (a) Calculate the binding energy per nucleon for 1 H and 1 H . The atomic masses (in amu) are 1 H , 2.01410, and 1 H ,
3.01605. melectron  0.000549 amu; mp 1.00728 amu; mn  1.00866 amu
(b) Which nuclide is more thermodynamically stable, 2H or 3H? Explain briefly.
For (a), see the Mastering Tutorial Problem with
hints (for credit) on PS10. (It is the second-tolast problem). Note that Tro approaches this
problem slightly differently (see Ppt comparison,
as well as Example 20.7 on p. 961)