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Home , Alpha decay, Binding energy, Decay energy, Electron capture, Electron emission, Nuclear binding energy

Chapter 24 : Nuclear Reactions and Their Applications 24.1 and Nuclear Stability

24.2 The Kinetics of Radioactive Decay

24.3 : Induced Changes in Nuclei

24.4 The Effects of Nuclear on

24.5 Applications of Radioisotopes

24.6 The Interconversion of and

24.7 Applications of Fission and Fusion Comparison of Chemical and Nuclear Reactions Chemical Reactions Nuclear Reactions 1. One substance is converted to 1. of one element typically another, but atoms never change change into atoms of another. identity. 2. Orbital are involved as 2. , , and other bonds break and form; nuclear particles are involved; orbital particles do not take part. electrons rarely take part. 3. Reactions are accompanied by 3.Reactions are accompanied by relatively small changes in energy relatively large changes in energy and no measurable changes in mass. and measurable changes in mass. 4. Reaction rates are influenced by 4. Reaction rates are affected by , concentration, number of nuclei, but not by catalysts, and the compound in temperature, catalysts, or the which an element occurs. compound in which an element Table 24.1 occurs. A + 0 ZX A - = p + n Z - number of protons(atomic no.) = p+ Number of neutrons(N) in a nucleus N = A - Z 238 0 92U N = 238 - 92 = 146 of n 238 - + 92U has 92e 92 p 235U - atomic bomb Subatomic elementary particles 0 -1 e

1 1 p 1 0n - nuclear species with specific numbers of two types of Nucleons - made up ofprotons and neutrons Properties of Fundamental Particles

• Particle Symbol Charge Mass • (x10-19 Coulombs) ( 10-27 kg) • Proton p +1.60218 1.672623

• Neutron n 0 1.674929

• Electron e -1.60218 0.0005486 NUCLEAR STABILITY Modes of Radioactive Decay

4 2+ • –heavy : 2He or • –neutron rich isotopes: e- or • emission–proton rich isotopes: • –proton rich isotopes: x-rays • Gamma-ray emission( )–Decay of nuclear excited states • –very heavy isotopes Fig. 24.1 (p. 1046) Alpha Decay–Heavy Elements

238 234 • U Th + a + e 9 t1/2 = 4.48 x 10

• 210Po 206Pb + a + e

t1/2 = 138 days • 256Rf 252No + a + e

t1/2 = 7 ms

• 241Am 237Np + a + e

t1/2 = 433 days Beta Decay–

• n p+ + b- + Energy

• 90Sr 90Y + b- + Energy

t1/2= 30 years • 14C 14N + b- + Energy

t1/2= 5730 years • 247Am 247Cm + b- + Energy

t1/2= 22 min • 131I 131Xe + b- + Energy

t1/2 = 8 days Electron Capture–

p+ + e- n + Energy = Electron capture p+ n + e+ + Energy = Positron emission

51Cr + e- 51V + Energy

t1/2 = 28 days 7Be 7Li + b+ + Energy

t1/2 = 53 days

177Pt + e- 177Ir + Energy

t1/2 = 11 s 144Gd 144Eu + b+ + Energy

t1/2 = 4.5 min Fig. 24.2 Number of Stable for Elements 48 through 54 of Element Number (Z) Nuclides

Cd 48 8

In 49 2

Sn 50 10

Sb 51 2

Te 52 8

I 53 1

Xe 54 9 Table 24.3 (p. 1049) Distribution of Stable Nuclides • Protons Neutrons Stable Nuclides %

• Even Even 157 58.8 • Even Odd 53 19.9 • Odd Even 50 18.7 • Odd Odd 7 2.6 Total = 267 100.0%

(c.f. Table 24.4, p. 1050) The 238U Decay Series

Fig. 24.3 CHEM 1332 Exam 1 is Friday Feb. 11 at 5:30 PM

Room 117 SR1

Web site http://www.uh.edu/~chem1p

User ID = chem1332 Password = ggw85p Predicting the Mode of Decay Unstable nuclide generally decays in a mode that shifts its N/Z ratio toward the band of stability. 1. Neutron-rich nuclides undergo ß decay, which converts a neutron into a proton, thus reducing the value of N/Z. 2. Proton-rich nuclides undergo positron decay or electron capture, thus increasing the value of N/Z. 3. Heavy Nuclides Z > 83 undergo alpha decay, thus reducing the Z and N values by two units per emission. 243 4 239 24.26 95Am 2He + 93Np

239 0 239 93Np -1ß + 94Pu

239 4 235 94Pu 2He + 92U

235 4 231 92U 2He + 90Th Kinetics of Radioactive Decay The decay rate or activity(A) = - N/ t N = Change in number of nuclei t = change in time SI unit of radioactivity is the (Bq), defined as one disintegration per second(d/s): 1Bq = 1 d/s 1 (Ci) equals the number of nuclei disintegrating each second in a 1g of - 226. 1 Ci = 3.70 X 1010 d/s For a large collection of radioactive nuclei,the number decaying per unit time is proportional to the number present: Decay rate (A) a N or A = kN k = decay constant The larger the value of k, the higher is the decay rate. A = -DN/Dt = kN The activity depends only on N raised to the first order so radioactivity decay is a first- order process. We consider the number of nuclei than their concentration. Half-life of Radioactive Decay t1/2

The half-life (t1/2) of a nuclide is the time it takes for half the nuclei present to decay. 14 14 0 6C 7N + -1ß The number of nuclei remaining is halved after each half-life. Natural Decay Series of Existing Isotopes

40K 40Ar 9 t1/2 = 1.29 x 10 years

232 Th 208 Pb 10 t1/2 = 1.4 x 10 years

235U 207 Pb 8 t1/2 = 7 x 10 years

238U 206 Pb 9 t1/2 = 4.5 x 10 years Natural Decay Series for -238

238U 234 Th

234Pa

234U 230 Th 226Ra 222Rn 218Po 214Pb

218At 214Bi 210 Tl

214Po 210Pb 206Hg

= a decay 210Bi 206Tl

= b- decay 210 Po 206Pb

238U: 8 decays and 6 decays leaves you with 206Pb Natural Decay Series for Uranium-235

235U 231 Th

231Pa 227Ac 223Fr 219At 215Bi

227 Th 223Ra 219Ra 215Po 211Pb

= decay 215At 211Bi 207 Tl = decay

211Po 207Pb

235U: 8 decays and 4 decays leaves you with 207Pb Natural Decay Series for -232

232 Th 228Ra

228Ac

228 Th 224Ra 220Rn 216Po 212Pb

= decay 212Bi 208Tl

= decay 212Po 208Pb

232 Th: 7 decays and 4 decays leaves you with 208Pb Fig. 24.A Decrease in Number of 14C Nuclei Over Time

Fig. 24.4 ln Nt / No = - kt ln No / Nt = kt No is the number of nuclei at t = 0 and Nt is the number of nuclei remaining at any time t.

To calculate the half-time ; set Nt = 1/2 N0 ln No / (1/2No) = k t 1/2 ; t 1/2 = ln2 / k The half-life is not dependent on the number of nuclei and is inversely related to the decay constant. Large k short t 1/2. Decay Constants (k) and Half-lives (t1/2) of Isotopes

Nuclide k t1/2

7 -2 4Be 1.30 x 10 / 53.3 day

8 16 -17 4Be 1.0 x 10 /s 6.7 x 10 s

9 4Be Stable

10 -7 6 4Be 4.3 x 10 /yr 1.6 x 10 yr

11 -2 4 Be 5.02 x 10 /s 13.8 s

Table 24.5 (p. 1054) Radioisotopic Dating

14 1 14 1 7N + 0n 6C + 1p

12C / 14C ratio is constant in living .

Dead 12C / 14C ratio increases.

14 14 14 0 C decays 6C 7N + -1ß for Determining the Age of Artifacts

Fig. 24.5 Nuclear Transmutation

14 4 1 17 7N + 2He 1H + 8O Notation 14N (a , p) 17O

27 4 1 30 13Al + 2He 0n + 15P

Notation 27Al(a , n) 30P Fig. 24.6A The Accelerator

Fig. 24.7 Formation of Some Transuranium Nuclides

Reaction Half-life of Product

239 4 240 1 1 94Pu + 2He 95Am + 1H + 2 0n 50.9 h

239 4 242 1 94Pu + 2He 96Cm + 0n 163 days

244 4 245 1 1 96Cm + 2He 98Bk + 1H + 2 0n 4.94 days

238 12 246 1 92U + 6C 98Cf + 4 0n 36 h

253 4 256 1 99Es + 2He 101Md + 0n 76 min

252 10 256 1 98Cf + 5B 103Lr + 6 0n 28 s

Table 24.6 (p. 1059) Fig. 24.8 Units of Radiation Dose rad = Radiation-absorbed dose The quantity of energy absorbed per kilogram of tissue: 1 rad = 1 x 10-2 J/kg rem = equivalent for man The unit of radiation dose for a human: 1 rem = 1 rad x RBE

RBE = 10 for a RBE = 1 for x-rays, g-rays, and b’s Examples of Typical Radiation Doses from Natural and Artificial Sources–I Source of Radiation Average Adult Exposure Natural Cosmic radiation 30-50 mrem/yr Radiation from the ground From clay soil and rocks ~25-170 mrem/yr In wooden houses 10-20 mrem/yr In brick houses 60-70 mrem/yr In concrete houses 60-160 mrem/yr Radiation from the air (mainly ) Outdoors, average value 20 mrem/yr In wooden houses 70 mrem/yr In brick houses 130 mrem/yr In light concrete houses 260 mrem/yr Internal radiation from in tap water and daily intake of food ~40 mrem/yr ( 40K, 14C, Ra) Table 24.7 (p. 1062) Examples of Typical Radiation Doses from Natural and Artificial Sources–II Source of Radiation Average Adult Exposure

Artificial Diagnostic x-ray methods Lung (local) 0.04-0.2 rad/film Kidney (local) 1.5-3.0 rad/film Dental (dose to the skin) £ 1 rad/film Therapeutic radiation treatment locally £ 10,000 rad Other sources Jet flight (4 hr) ~1 mrem Nuclear tests < 4 mrem/yr Nuclear power industry < 1 mrem/yr

Total Average Value 100-200 mrem/yr Table 24.7 (p. 1062) Acute Effects of a Single Dose of Whole-Body Irradiation–I Dose Lethal Dose (rem) Effect Population (%) No. of Days

5-20 Possible late effect; possible — — chromosomal aberrations 20-100 Temporary reduction in — — white blood cells 50+ Temporary sterility in men — — (100+ rem = 1 yr duration) 100-200 “Mild radiation sickness”: vomiting, diarrhea, tiredness in a few hours Reduction in infection resistance Possible bone growth retardation in children Table 24.8 (p. 1063) Acute Effects of a Single Dose of Whole-Body Irradiation–II Dose Lethal Dose (rem) Effect Population (%) No. of Days

300+ Permanent sterility in women — —

500 “Serious radiation sickness”: 50-70 30 marrow/intestine destruction

400-1000 Acute illness, early deaths 60-95 30

3000+ Acute illness, death in hours 100 2 to days

Table 24.8 (p. 1063) (p. 1064) 24.6 Inter conversion of Mass and Energy : A heavy nucleus splits into two lighter nuclei. : Two lighter nuclei combine to form a heavier one. The Mass Defect (Dm) - The mass decrease that occurs when nucleons combine to form a nucleus The size of the mass change is nearly 10 million times that of bond breakage. NUCLEAR ENERGY

• EINSTEIN’S EQUATION FOR THE CONVERSION OF MASS INTO ENERGY

• E = mc2

• m = mass (kg)

• c =

• c = 2.998 x 108 m/s Nuclear

Energy required to break up 1 mol of nuclei into their individual nucleons.

Nucleus + nucleons

For 12C DE = Dmc2 = (9.894 x 10-5kg/mol)(2.9979 x108m/s)2 = 8.8921 x 1012 J/mol Fig. 24.12 Units Used for Nuclear Energy Calculations

Electron volt (ev) The energy an electron acquires when it moves through a potential difference of one volt:

1 ev = 1.602 x 10-19J

Binding are commonly expressed in units of megaelectron volts (Mev)

1 Mev = 106 ev = 1.602 x 10 -13J

A particularly useful factor converts a given mass defect in units to its energy equivalent in electron volts: 1 amu = 931.5 x 106 ev = 931.5 Mev Binding Energy per of Deuterium has a mass of 2.01410178 amu.

Hydrogen = 1 x 1.007825 amu = 1.007825 amu Neutrons = 1 x 1.008665 amu = 1.008665 amu 2.016490 amu Mass difference = theoretical mass - actual mass = 2.016490 amu - 2.01410178 amu = 0.002388 amu Calculating the binding energy per nucleon:

Binding energy 0.002388 amu x 931.5 Mev/amu = Nucleon 2 nucleons

= 1.1123 Mev/nucleon Calculation of the Binding Energy per Nucleon for -56 The mass of iron-56 is 55.934939 amu; it contains 26 protons and N = A - Z 30 neutrons Theoretical mass of Fe-56 : atom mass = 26 x 1.007825 amu = 26.203450 amu Neutron mass = 30 x 1.008665 amu = 30.259950 amu 56.463400 amu Mass defect = theoretical mass - actual mass:

56.463400 amu - 55.934939 amu = 0.528461 amu

Calculating the binding energy per nucleon: Binding energy 0.528461 amu x 931.5 Mev/amu = Nucleon 56 nucleons = 8.7904 Mev/nucleon Calculation of the Binding Energy per Nucleon for Uranium-238

The actual mass of uranium-238 = 238.050785 amu; it has 92 protons and 146 neutrons N = A - Z Theoretical mass of uranium-238: mass = 92 x 1.007825 amu = 92.719900 amu Neutron mass = 146 x 1.008665 amu = 147.265090 amu 239.98499 amu Mass defect = theoretical mass - actual mass: 239.98499 amu - 238.050785 amu = 1.934205 amu

Calculating the binding energy per nucleon: Binding energy 1.934205 amu x 931.5 Mev/amu = Nucleon 238 nucleons = 7.5702 Mev/nucleon Mass and Energy in Nuclear Decay–I

212 Consider the alpha decay of Po t1/2 = 0.3 ms

212Po 208Pb + a + Energy

211.988842 g/mol 207.976627 g/mol + 4.00151 g/mol Products = 207.976627 + 4.00151 = 211.97814 g/mol

Mass = Po - Pb + a = 211.988842 -211.97814 0.01070 g/mol

E = mc2 = (1.070 x 10-5 kg/mol)(3.00 x 108m/s)2 = 9.63 x 1011 J/mol

11 9.63 x 10 J/mol = 1.60 x 10-12J/atom 6.022 x 1023 atoms/mol Mass and Energy in Nuclear Decay–II

The energy for the decay of 212Po is 1.60 x 10-12J/atom

-12 1.60 x 10 J/atom = 1.00 x 107 ev/atom 1.602 x 10-19 J/ev

10.0 x 106 ev 1.0 x 10-6 Mev x = 10.0 Mev/atom atom ev

The of the from 212Po is 8.8 Mev. Fig. 24.13 Fig. 24.14 Critical Mass: Mass needed to achieve a . Fig. 24.15B Neutron Induced Fission– Bombs and Reactors There are three isotopes with sufficiently long half-lives and significant fission cross-sections that are known to undergo neutron induced fission, and are useful in fission reactors, and nuclear weapons. Of these, only one exists on (235U which exists at an abundance of 0.72% of ) and that is the that we use in nuclear reactors for and some weapons. The three isotopes are:

233 5 U t1/2 = 1.59 x 10 years sigma fission = 531 barns

235 8 U t1/2 = 7.04 x 10 years sigma fission = 585 barns

239 5 Pu t1/2 = 2.44 x 10 years sigma fission = 750 barns Breeding

There are two relatively common heavy isotopes that will not undergo neutron induced fission, that can be used to make other isotopes that do undergo neutron induced fission, and can be used as nuclear fuel in a . Natural thorium is 232 T which is common in rocks.

232 1 233 Th + 0n Th + Energy t1/2 = 22.3 min 233 233 - Th Pa + b + Energy t1/2 = 27.0 days 233 233 - 5 Pa U + b + Energy t1/2 = 1.59 x 10 years

Natural uranium is 238U which is common in rocks as well.

238 1 239 U + 0n U + Energy t1/2 = 23.5 min 239 239 - U Np + b + Energy t1/2 = 2.36 days 239 239 - Np Pu + b + Energy t1/2 = 24400 years Hydrogen Burning in and Nuclear Weapons

1H + 1H 2H + b+ + 1.4 Mev

1H + 2H 3He + 5.5 Mev

2H + 2H 3He + 1n + 3.3 Mev

2H + 2H 3H + 1H + 4.0 mev

2H + 3H 4He + 1n + 17.6 Mev Easiest! Highest 2H + 3He 4He + 1H + 18.3 Mev cross- section! 1H + 7Li 4He + 4He + 17.3 Mev Burning Reactions in Stars

12C + 4He 16O

16O + 4He 20Ne

20Ne + 4He 24Mg

24Mg + 4He 28Si

28Si + 4He 32S

32S + 4He 36Ar

36Ar + 4He 40Ca Element Synthesis in the Life Cycle of a

Fig. 24.C (p. 1077) The Design for Magnetic Containment of a Fusion Plasma

Fig. 24.16 24.42

3 -4 -1 k = 0.693/t 1/2 = 0.693/1.6 x 10 yr = - 4.331x10 yr

ln Nt / No = -kt

t = ln (0.185g/2.50g) / -4.33 x 10-4 yr-1 = 6.01 x105 yr

24.44

k = 0.693/5730yr = 1.21 x 10-4 yr-1

-4 -1 t = ln (Nt/No)/ -k = ln(0.735/1.000)/ -1.21x10 yr

t = 2.54 x 10 3 yr