Chapter 19 - Nuclear Chemistry...
Transcript of Chapter 19 - Nuclear Chemistry...
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Chapter 19 - Nuclear Chemistry Applications
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Rates of Radioactive Decay
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Half-life - The time it takes for half of the parent nuclides in a radioactive sample to decay to the daughter nuclides
The amount that remains after one half-life is always one-half
of what was present at the start.
The amount that remains after two half-lives is one-quarter of what was present at the start.
A radioactive sample does not decay to zero atoms in two half-lives—You can’t add two half-lives together to get a “whole”
life.
The Concept of Half-life
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A plot of the number of Th-232 atoms in a sample initially containing 1 million atoms
as a function of time.
Th-232 has a half-life of 14 billion years.
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Half-Life
Each radioactive nuclide has a unique half-life that is not affected by physical conditions or chemical environment.
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Radioactive Decay Half-Life
“I-131 decays by beta emission with a half life of 8 days.” ?
131 53
I0
-1e
131 54
Xe➔ +
1) What is meant by
131 53 I1.000 g
131 54 Xe
131 53 I0.500 g
0.500 g131
54 Xe
131 53 I0.250 g
0.750 g131
54 Xe
131 53 I0.125 g
0.875 g
8 days
8 days
8 days
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2) The half-life of the beta particle emitter tritium, 3H, is 12 years. How much of a 1.00 g sample of 3H remains after 48 years?
1.00 g ➝0.50 g ➝0.250 g ➝ ➝0.125 g 0.0625 g
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Radioactive Decay
n = t/t½ (t½ = half-‐life) Nt/No = 0.5n
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Half-Life
half of the radioactive atoms decay each half-life
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First Order Reactions
Rate = k[A] ln[A] = -kt +ln[A]0 (integrated rate law)
graph of ln[A] vs t is straight line (slope = -k and y intercept = ln[A]0)
t½ = ln2/k = (0.693)/k (constant half-life)
• Rate = k[A]0 = k
constant rate reactions
• [A] = -kt + [A]0
• graph of [A] vs. time is straight line with slope = -k and y-intercept = [A]0
• t ½ = [A0]/2k
• when Rate = M/sec, k = M/sec
[A]0
[A]
time
slope = - k ln[A]
ln[A]0
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ln[N]t - ln[N]0 = -kt
Radioactive Decay-A First Order Process
[N]t
[N]0ln = -kt [N]t = [N]0 x e-kt
t½ = 0.693 k
k = 0.693
t½
ln[N]t = -kt + ln[N]0 [N] = number of radioactive nuclei [N] = intensity of radioactivity
ln[A]t = -kt + ln[A]0 [A]t = conc A at time t[A]0 = conc A at time 0
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3) If you have a 1.35 mg sample of Pu-236, calculate the mass of Pu-236 that will remain after 5.00 years.
t½ = 0.693
k k =
0.693 t½ =
0.693 2.86 y = 0.242 yr-1
ln = Nt N0
-kt
Nt = N0 e-kt = N0 e-(0.242 yr-1)(5.00 yr)
Nt = N0 e-kt = (1.35 mg)e -(0.242 yr-1)(5.00 yr)
Nt = N0 e-kt = 0.402 mg
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4) Radioactive radon-222 decays with a loss of one α particle. The half-life is 3.82 days. What percentage of the radon in a sealed vial would remain after 7.0 days?
t½ = 0.693
k k = 0.693 t½ =
0.693 3.82 d = 0.181 d-1
ln = Nt N0
-(0.181 d-1)(7.0 d)
Nt N0
= e-kt = e-(0.181 d-1)(7.0 d)
= e -(1.27)
Nt N0
= 0.28 = 28%
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Artifact Dating
Mineral (geological)
Compare amount of U-238 (t½ = 4.5 x 109 yr) to Pb-206
Compare amount of K-40 (t½ = 1.25 x 109 yr) to Ar-40
Archeological (once living materials)
Compare amount of C-14 (t½ = 5730 yr) to C-12
While a substance is living C-14/C-12 ratio is constant (CO2 exchange with the atmosphere continues).
When an organism dies, C-14/C-12 ratio decreases.
Useful to up to about 50,000 yr
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5) An artifact contains 12.5% of the original amount of C-14. How old is this sample? (C-14 half-life is 5730 years.)
100 % ➝ 50 % ➝ 25 % ➝ ➝12.5 % 6.25 %
3 x 5730 = 17,200
% C-14 (relative to
living organism)
Number of
Half-Lives
Time
(yrs)
100.0 0 0
50.0 1 5,730
25.00 2 11,460
12.50 3 17,190
6.250 4 22,920
3.125 5 28,650
1.563 6 34,380
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Radiometric Datingn = t/t1/2
t = time t1/2 = time for a half-life n = the number of half-lives
Nt/No = 0.5n
No = amount initially present Nt = amount at time t n = the number of half-lives
If we know what fraction of sample is left (Nt/No) and its half-life (t1/2), we can calculate how much time has elapsed.
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6) A mammoth tusk containing grooves made by a sharp stone edge (indicating the presence of humans or Neanderthals) was uncovered at an ancient campsite in the Ural Mountains in 2001. The 14C/12C ratio in the tusk was only 1.19% of that in modern elephant tusks. How old is the mammoth tusk?
ln = 1.19 100
-(1.21 x 10-4 yr-1 )(t)
k = 0.693
5730 yr
k = 1.21 x 10-4 yr-1
k = 0.693
t½ ln =
Nt N0
-kt
(-4.43) /-(1.21 x 10-4) = t = 36,600 yr
Nt/No = 0.5n
.0119 = 0.5n
log(0.0119) = nlog(0.5)
-1.92 = (n)(-0.301)
n = 6.38 = # half-lives
yr = (6.38)(5730)
yr = 36,600
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7) An ancient skull gives a 4.50 disintegrations / min gC. If a living organism gives 15.3 disintegration / min gC, how old is the skull ?
Kinetics of Radioactive Decay
• Rate = kN
N = number of radioactive nuclei
• t1/2 = 0.693/k
• the shorter the half-life, the more nuclei decay
every second – we say the sample is hotter
k = 1.21 x 10-4 yr-1
ln rate1 rate2
= -kt t =
4.50 15.3
dis/min gCdis/min gC
ln
-1.21 x 10-4 yr-1
t = 10,000 yr
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Measuring Radioactivity
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Quantities of Radiation
Parameter' Unit' Descrip/on'
Level'of'radioac/vity' Becquerel'(Bq)*' 1'disintegra/on/s'
Curie'(Ci)'3.7'×'1010'nuclear'disintegra/ons/s'
Ionizing'energy'absorbed'
Gray'(Gy)'1'Gy'='1'J/kg'of'/ssue'mass'
Amount'of'/ssue'damage'
Sievert'(Sv)' 1Sv'='1'Gy'×'RBE**'
*SI'unit'of'radioac/vity;'**Rela/ve'Biological'Effec/veness'
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Biological Effects of Radioactivity
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Sources of Radiation
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Acute&Effects&of&Single&Whole3Body&Doses&of&Ionizing&Radia<on&
Dose&(Sv)&
Toxic&Effect&
0.05–0.25&
No´&effect,&possible&carcinogenic&or&mutagenic&damage&to&DNA&
0.25–1.0&Temporary&reduc<on&in&white&blood&cell&
count&
1.0–2.0&Radia<on&sickness:&fa<gue,&vomi<ng,&diarrhea,&impaired&immune&system&
2.0–4.0&Severe&radia<on&sickness:&intes<nal&bleeding,&
bone&marrow&destruc<on&
4.0–10.0&Death,&usually&through&infec<on,&within&
weeks&
>10.0& Death&within&hours&
Biological Effects of Radioactivity
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Medical Applications of Radionuclides
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Medical Applications of Radionuclides
Therapeutic Agents Imaging Agents
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Positron Emission
C-11 B-11
β+
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Positron = “antimatter”
Energy of matter/antimatter reaction related to mass defect.
Energy of nuclear reaction released as gamma rays.
What are positrons ?
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Positron Emission
β+ antimatter
β- matter
photon 511 kev
photon 511 kev
Detector Det
ecto
r
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Positron Emission Tomography
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Positron Emission Tomography
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PET study revealing differences in brain metabolism in recovering alcoholic (left, 10 days, and right, 30 days,
after withdrawal)
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Nuclear Fission
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On January 6, 1939, Meitner, Strassmann, and Hahn reported that the neutron bombardment of uranium resulted in nuclear fission—the splitting
of the atom.
U235 92n1
0 Ba142 56 K91
36 n1 03+ + +
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Nonradioactive Nuclear ChangesSome nuclei are inherently unstable.
If their nuclei are hit by a neutron, the large nucleus splits into smaller nuclei
This is called fission
Small nuclei can be accelerated to such a degree that they overcome their charge repulsion and smash together.
A larger nucleus is formed.
This is called fusion
Both fission and fusion release large amounts of energy
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Nuclear fission:
A nuclear reaction in which the nucleus of an element splits into two lighter nuclei;
The process is usually accompanied by the release of one or more neutrons and energy.
U235 92 n1
0 Ba142 56 K91
36 n1 03+ + +
U235 92 n1
0 Cs138 55 Rb96
37 n1 02+ + +
U235 92 n1
0 Te137 52 Zr97
40 n1 02+ + +
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Fissionable Materials
U-235, Pu-239, and Pu-240
Natural uranium is less than 1% U-235
Mostly U-238
Not enough U-235 to sustain a chain reaction
To produce fissionable uranium, natural uranium must be enriched in U-235
to about 3% for “reactor grade”
to about 7% for “weapons grade”
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Fission Chain Reaction
A chain reaction occurs when a reactant in a process is also a product of the process.
In the fission process, the neutrons are both.
Only a small number of neutrons are needed to start the chain.
Many neutrons produced in fission are either ejected from the uranium before they hit another U-235 or are absorbed by the surrounding U-238
The minimum amount of fissionable isotope needed to sustain the chain reaction is called the critical mass.
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Fission Chain Reaction
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Nuclear Power Plants: Controlled Fission
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In essence, the Little Boy design consisted of a gun that fired one mass of uranium 235 at another mass of uranium 235, thus creating a supercritical mass. A crucial requirement was that the pieces be brought together in a time shorter than the time between spontaneous fissions. Once the two pieces of uranium are brought together, the initiator introduces a burst of neutrons and the chain reaction begins, continuing until the energy released becomes so great that the bomb simply blows itself apart.
Little Boy
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The initial design for the plutonium bomb was also based on using a simple gun design (known as the "Thin Man") like the uranium bomb. The plutonium, however, contained small amounts of plutonium 240, an isotope with a rapid spontaneous fission rate. A gun-type bomb would not be fast enough to work. Before the bomb could be assembled, stray neutrons would have been emitted from the spontaneous fissions, and would start a premature chain reaction, leading to a great reduction in the energy released.
Seth Neddermeyer, a scientist at Los Alamos, developed the idea of using explosive charges to compress a sphere of plutonium very rapidly to a density sufficient to make it go critical and produce a nuclear explosion.
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Nuclear Fusion
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Nuclear fusion – nuclear reaction in which sub-atomic particles or atomic nuclei collide and fuse together, forming more massive nuclei and releasing energy.
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Nuclear Fusion
Fusion is the combining of light nuclei to make heavier nuclei.
The source of the sun’s energy
Requires a high input of energy to initiate the process
Produces 10 times the energy of fission per gram
No radioactive byproducts
The only currently working application is the H-bomb.
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Nuclear Fusion
Deuterium-Tritium Fusion Reaction
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Artificial Transmutation
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Artificial Transmutation
Bombardment of one nucleus with neutrons or another nucleus causing new atoms to form
Requires a “particle accelerator”
Ex: Tc-97 is made by bombarding Mo-96 with deuterium:
Mo96 42H2
1 Tc97 43 n1
0+ +
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Formation of Transuranium Nuclides
Pu239 94He4
2 Am240 95 H1
1+ + n1 0+ 2
Pu239 94He4
2 Cm242 96+ + n1
0
Cm244 96He4
2 Bk245 97 H1
1+ + n1 0+ 2
U238 92C12
6 Cf246 98+ + n1
04
Es253 99He4
2 Md256 101+ + n1
0
Cf252 98B10
5 Lr256 103+ + n1
06
Cf249 98H2
1 Es248 99+ + n1
03 25 min
51 hr
163 d
5 d
36 h
76 min
28 sec