Chapter 21 - Nuclear Chemistry Applications

Rates of Radioactive Decay

The Concept of Half-life 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 halflives You can t add two half-lives together to get a whole life.

Th-232 has a half-life of 14 billion years. A plot of the number of Th-232 atoms in a sample initially containing 1 million atoms as a function of time.

Half-Life Each radioactive nuclide has a unique half-life that is not affected by physical conditions or chemical environment.

Radioactive Decay Half-Life 1) What is meant by I-131 decays by beta emission with a half life of 8 days.? 131 53 I 0-1 e 131 + 54 Xe 1.000 g 131 53 I 8 days 0.500 g 0.500 g 131 53 I 131 54 Xe 8 days 0.250 g 0.750 g 131 53 I 131 54 Xe 8 days 0.125 g 0.875 g 131 53 I 131 54 Xe

2) The half-life of the beta particle emitter tritium, 3 H, is 12 years. How much of a 1.00 g sample of 3 H remains after 48 years? 1.00 g 0.50 g 0.250 g 0.125 g 0.0625 g

Radioactive Decay n = t/t ½ (t ½ = half- life) N t /N o = 0.5 n

Half-Life half of the radioactive atoms decay each half-life

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) ln[a] 0 [A] 0 [A] ln[a] slope = - k time

Radioactive Decay-A First Order Process ln[a]t = -kt + ln[a]0 ln[n]t = -kt + ln[n]0 [A]t = conc A at time t [A]0 = conc A at time 0 [N] = number of radioactive nuclei [N] = intensity of radioactivity t½ = 0.693 k k = 0.693 t½ ln[n]t - ln[n]0 = -kt ln [N]t [N]0 = -kt [N]t = [N]0 x e -kt

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. t ½ = 0.693 k k = 0.693 t ½ = 0.693 2.86 y = 0.242 yr-1 N t ln = N 0 -kt N t = N 0 e -kt = e -(0.242 yr-1 )(5.00 yr) N t = N 0 e -kt = (1.35 mg)e -(0.242 yr-1 )(5.00 yr) N t = N 0 e -kt = 0.402 mg

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? t ½ = 0.693 k k = 0.693 t ½ = 0.693 3.82 d = 0.181 d-1 N t ln = N 0 -(0.181 d -1 )(7.0 d) N t N = e-kt = e -(0.181 d-1 )(7.0 d) 0 = e -(1.27) N t N 0 = 0.28 = 28%

Artifact Dating Mineral (geological) Compare amount of U-238 (t½ = 4.5 x 10 9 yr) to Pb-206 Compare amount of K-40 (t½ = 1.25 x 10 9 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

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.) 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 34,380 100 % 50 % 25 % 12.5 % 6.25 %

Radiometric Dating n = t/t 1/2 t = time t 1/2 = time for a half-life n = the number of half-lives N t /N o = 0.5 n N o = amount initially present N t = amount at time t n = the number of half-lives If we know what fraction of sample is left (N t /N o ) and its half-life (t 1/2 ), we can calculate how much time has elapsed.

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 14 C/ 12 C ratio in the tusk was only 1.19% of that in modern elephant tusks. How old is the mammoth tusk? k = 0.693 t½ k = 1.19 ln = 100 0.693 5730 yr N t ln = N 0 k = 1.21 x 10-4 yr -1 -kt -(1.21 x 10-4 yr -1 )(t) (-4.43) /-(1.21 x 10-4 ) = t = 36,600 yr N t /N o = 0.5 n.0119 = 0.5 n log(0.0119) = nlog(0.5) -1.92 = (n)(-0.301) n = 6.38 = # half-lives yr = (6.38)(5730) yr = 36,600

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? k = 1.21 x 10-4 yr -1 ln rate 1 rate2 = -kt t = ln 4.50 15.3 dis/min gc dis/min gc -1.21 x 10-4 yr -1 t = 10,000 yr

Measuring Radioactivity

Quantities of Radiation Parameter' Unit' Descrip/on' Level'of'radioac/vity' Becquerel'(Bq)*' 1'disintegra/on/s' Ionizing'energy' absorbed' Amount'of'/ssue' damage' Curie'(Ci)' Gray'(Gy)' Sievert'(Sv)' 3.7' '10 10 'nuclear' disintegra/ons/s' 1'Gy'='1'J/kg'of' /ssue'mass' 1Sv'='1'Gy' 'RBE**' *SI'unit'of'radioac/vity;'**Rela/ve'Biological'Effec/veness'

Biological Effects of Radioactivity

Sources of Radiation

Biological Effects of Radioactivity Acute&Effects&of&Single&Whole3Body&Doses&of&Ionizing& Radia<on& Dose& (Sv)& 0.05 0.25& 0.25 1.0& 1.0 2.0& 2.0 4.0& 4.0 10.0& >10.0& Toxic&Effect& No&acute&effect,&possible&carcinogenic&or& mutagenic&damage&to&dna& Temporary&reduc<on&in&white&blood&cell& count& Radia<on&sickness:&fa<gue,&vomi<ng,& diarrhea,&impaired&immune&system& Severe&radia<on&sickness:&intes<nal&bleeding,& bone&marrow&destruc<on& Death,&usually&through&infec<on,&within& weeks& Death&within&hours&

Medical Applications of Radionuclides

Medical Applications of Radionuclides Therapeutic Agents Imaging Agents

Positron Emission β+ C-11 B-11

What are positrons? Positron = antimatter Energy of matter/antimatter reaction related to mass defect. Energy of nuclear reaction released as gamma rays.

Detector Positron Emission β+ antimatter Detector photon 511 kev photon 511 kev β- matter

Positron Emission Tomography

PET study revealing differences in brain metabolism in recovering alcoholic (left, 10 days, and right, 30 days, after withdrawal

Nuclear Fission

On January 6, 1939, Meitner, Strassmann, and Hahn reported that the neutron bombardment of uranium resulted in nuclear fission the splitting of the atom. 1 235 n U Ba 0 92 142 91 1 K 3 n 56 36 0 + + +

Nonradioactive Nuclear Changes Some 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

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.

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

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. Man 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.

Fission Chain Reaction

Nuclear Power Plants: Controlled Fission

Little Boy 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.

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.

Nuclear Fusion

Nuclear fusion nuclear reaction in which sub-atomic particles or atomic nuclei collide and fuse together, forming more massive nuclei and releasing energy.

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.

Nuclear Fusion Deuterium-Tritium Fusion Reaction

Artificial Transmutation

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: 2 96 H Mo Tc 1 42 97 1 n 43 0 + +

Formation of Transuranium Nuclides 4 239 240 1 H 95 1 He Pu Am 2 94 + + + 2 n 1 0 51 hr 4 239 He Pu Cm 2 94 96 4 + + n 244 242 1 0 245 1 H 97 1 246 1 4 98 0 He Cm Bk 2 96 12 + + + 2 n 238 C U Cf 6 92 2 + + n 249 248 H Cf Es 1 98 99 + + n 1 0 1 0 163 d 5 d 36 h 3 25 min 4 10 253 256 He Es Md 2 99 101 + + n 252 256 B Cf Lr 5 98 103 + + 6 n 1 0 1 0 76 min 28 sec