04/10/231

Radioactivity

Spontaneous emission of small particles and/or radiation (energy) by unstable atomic nuclei to attain more stable nuclear state

04/10/232

Chemical Reactions Nuclear Reactions

Electrons react outside nucleus Protons/neutrons/electrons/other elementary particles involved

Same # of each kind of element appears in reactants and products (atoms rearranged by breaking/forming chemical bonds)

Elements transmute into other elements

Isotopes react similarly Isotopes react differently

Dependent on chemical combination Independent on chemical combination

Mass reactants = mass products Mass changes detectable

Reactions accompanied by absorption or release of relatively small amounts of energy

Reactions accompanied by absorption or release of tremendous amounts of energy

Rates of reactions influenced by temperature, pressure, concentration, and catalysts

Rates of reaction normally not affected by temperature, pressure, and catalysts

04/10/233

• Nuclide: nucleus with specified number of protons and neutrons

– Symbolized as AzX

• X - symbol of element• A - mass number = nuclear mass• Z - atomic number = nuclear charge

• Isotope: nuclides with same atomic # but different mass #s

04/10/234

• Radionuclide:– Radioactive nuclide (unstable nucleus)– Radioactive isotope ( radioisotope): isotope

w/radioactive nuclide

• Radioactive decay: process of all radioactive decay until isotope with stable nucleus is reached

• Transmutation: nucleus reacts with another nucleus, elementary particle, or photon (gamma particle) to produce one or more new nuclei

• Nuclear equation: representation of change that occurs within or among atomic nuclei

04/10/23 5

Balancing rules for nuclear equations

• Sum of mass #s of reactants must equal sum of mass #s of products (conservation of mass number)

– 14 + 4=18=17 + 1 • Sum of nuclear charges of reactants must

equal sum of nuclear charges of products (conservation of atomic number)

– 7 + 2 = 9 = 8 + 1

04/10/23 6

Property Alpha (α) Beta (β-) Gamma (γ ) Proton Positron (β+) Neutrons 10n X-rays

Charge 2+ 1- 0 1+ 1+ 0 0

Mass 6.64 x 10-24 g 9.11 x 10-28 g 0 1.6725 × 10-24 g 9.11 x 10-28 g 1.6750 × 10-24 g

Relative penetrating power

1 100 10,000 100 High High

Nature of radiation

42He

nucleus

0-1e

electrons

High-energy photons

11H

nucleus of H-1 atom

0+1e

10n

How far they travel

•Few cm in air (colliding w/ air molecules)•Lose KE and electrons to become ordinary He

•Up to 300 cm in air (collide less w/air molecules because very small)

•Highly penetrating EM radiation easily passing through most objects

•Not able to penetrate matter to significant extent

•Very penetrating (no charge)

•Highly penetrating EM radiation that can penetrate through body

Stopped by •High ionizing power•Do not penetrate skin•Stopped w/piece of paper•Harmful if ingested

•Moderate ionizing power•Can penetrate skin•Stopped by aluminum foil thicker than 3 mm•Skin burns, harmful if ingested

•Almost no ionizing power•Few cm lead or m of concrete•Dangerous because very penetrating

•Antimatter, so annihilated when encounter electron

•Materials w/high H content•Causes significant damage when collisions occur by producing gamma rays through interactions w/tissue atoms

04/10/23 7

Alpha emission

Beta emission

Positron emission

Electron capture

Gamma rays

What is emitted

42α

0-1β (electron) 0

+1β (Electron

w/+ charge)

0-1e (X-ray

photon)

00γ

How Emission of 42He

N P/ elec-tron emitted (1

0n 0-1β +

11p + energy)

P N w/positron emitted (1

1p 0-1β + 1

0n)

Captured low energy inner-shell electron + P N (0

-1e

+ 11p 1

0n +

energy)

Emission of EM radiationNuclear isomer (m next to mass) in excited stateReturns to ground state when photon released

What happens

Mass (-4) 4Atomic # (-2)

Mass sameAtomic # (+1)

Mass sameAtomic # (-1)

Mass sameAtomic # (-1)

No change mass/#

What elements emit these

Heavy iso-topes (> 83)Reduce #P/N

Neutron rich isotopes

Proton rich isotopes

Proton rich isotopes

Most all unstable isotopes

Example

04/10/23 8

Nuclear Stability

• Neutron-to-proton ratio– Low atomic numbers

• Ratio close to 1• Fall in zone of stability

– Atomic # increases (21-83)• Z > 20, #N always exceeds #P protons in stable

isotopes• Ratio gradually increases from 1 to 1.5

– > 83 (Bismuth) no stable nuclides• All radioactive and their isotopes decay• Lie outside zone of stability

Hg: atomic mass = 200atomic # = 80

#P = 80, #N = 120 N/P ratio is 120/80 = 1.50

04/10/23 9

alpha emissionbeta emission

positron emission and electron capture

• What is emitted depends upon location by zone of stability

– Left of zone (mass # > atomic wt)• Neutron rich (tries to gain protons/lose

neutrons) – NP + beta particle• Decays by β emission

– Right of zone (mass # < atomic wt)• Proton rich (tries to lose protons/gain

neutrons) – PN + positron• Decays by positron emission/electron capture

– On zone, but Z>83• Often decay by emitting alpha particles

(usually above 60)04/10/23 10

04/10/23 11

• 24196Cf undergoes electron capture

• 24196Cf + 0

-1e 24195Am

• 24195Am produces an α particle

• 24195Am 241

93Np + 42He

• 12154Xe produces a β particle

• 12154Xe 121

53I + 01e

• 16467Ho + 0

-1e ?• 164

67Ho + 0-1e 164

66Dy• 158

67? 15866Dy + 0

1e• 158

67Ho 15866Dy + 0

1e• 242

94Pu 23892U + ?

• 24294Pu 238

92U + 42He

04/10/23 12

• Magic Numbers– Isotopes w/even # nucleons (P + N) tend to be

more stable than those w/odd # nucleons– Nuclei w/certain specific # P/N within nucleus

ensure extra degree of stability– Nucleus much less likely to absorb additional

neutron– Magic numbers for P/N are 2/8/20/28/50/82/126

• Correspond to filling of shells in structure of nucleus• When nuclei has P/N both in magic numbers, very stable

and in high abundance in universe

• 3015P < 39

20Ca < 4020Ca

– P-30-least stable-odd #s of both P/N – C-39-even #P (20)/odd #N-even #P and "magic number"-more

stable than P-30– Ca-40-most stable-even #P/N-both #s "magic numbers"

04/10/23 13

11 1

1 2 11 3 3 1

1 4 6 4 11 5 10 10 5 1

1 6 15 20 15 6 11 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 11 9 36 84 126 126 84 36 9 1

          

1             = 1   2

5 - 1         = 4   8

15 - 4 - 1     = 10   20

35 - 10 - 5 - 6 = 14   28

70 - 20 - 15 - 10 = 25   50

126

- 35 - 35 - 15 = 41   82

210

- 56 - 70 - 21 = 63   126

     

Pascal`s Triangle

04/10/23 14

• Odd-even rule– When #N/P both even numbers, isotopes

tends to be far more stable than when they are both odd

– Of all 264 stable isotopes, number of protons/neutrons• 168-even/even• 57-even/odd• 50-odd/even• 4-odd/odd

Radioactive series (nuclear disintegration series)

• Some nuclei cannot gain stability w/single emission

04/10/23 15

04/10/23 16

Z > 83 --  alpha 92U 238 => 90Th234 + 2He4  

unpredicted Beta 90Th234 =>  91Pa234 + -1eo 

unpredicted  Beta 91Pa234 =>  92U234 + -1e

o

Z > 83 --  alpha 92U234 => 90Th230 + 2He4

Z > 83 --  alpha 90Th230 => 88Ra226 + 2He4

Z > 83 --  alpha 88Ra226 => 86Rn222 + 2He4 

Z > 83 --  alpha 86Rn222 => 84Po218 + 2He4 

Z > 83 --  alpha 84Po218 => 82Pb214 + 2He4 

Beta 82Pb214 => 83Bi214 + -1eo 

Beta 83Bi214 => 84Po214 + -1eo 

Z > 83 --  alpha 84Po214 => 82Pb210 + 2He4 

Beta  82Pb210 => 83Bi210 + -1eo 

Beta 83Po210 => 84Po210 + -1eo

Z > 83 --  alpha 84Po210 => 82Pb206 + 2He4 

stable  82Pb206

24797Bk undergoes decay to what element after ααβααβαβααααββα?

Nuclear Transmutations

• Nuclear reactions induced by nucleus gaining neutron or another nucleus

• Converts nucleus into another nucleus

• Can be represented by listing, in order, target nucleus, bombarding particle, ejected particle, and product nucleus

04/10/23

17

04/10/23 18

Homework:

Read 18.1, pp. 877-882

Q pp. 906-907, #9a, 10, 12, 14, 16, 18

04/10/23 19

Rates of decay• Unstable atomic nucleus loses energy by emitting

radiation– Spontaneous– Without collision w/another particle

• Radioactive decay rates obey first-order kinetics– Instantaneous rate of decay of N radioactive

atoms is directly proportional to # atoms present at that instant in time

• Unit of activity– Becquerel (bq) – SI unit

• 1 Bq is one transformation (decay) per second

– Curie (Ci)• Originally based on activity of 1 g radium (1

Ci = 3.7 x 1010 Bq)

Radioactivity of substance may be measured decay rate

• Decay rate = # atoms disintegrating per unit time = λN– λ (k) = first-order rate

constant (decay constant)– N = # atoms of

particular radioisotope present in sample

– X = concentration of reactant at any moment

– Xo = initial concentration

• Integrated first-order equation– N = # atoms of

radioisotope present in sample after time t has elapsed

– N0 = # atoms of radioisotope present initially

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04/10/23 21

• Rate constant for 14C is much larger than rate constant for 238U– 14C: k = 1.210 x 10-4 yr-1

– 238U: k = 1.54 x 10-10 yr-1 – Therefore, 14C decays much faster than 238U

• Half life for decay of 14C is much shorter than that of 238U– 14C: t1/2 = 5730 yr

– 238U: t1/2 = 4.51 x 109 yr

– Therefore, 14C decays much faster than 238U

04/10/23 22

Half-life

• Time it takes for exactly half of nuclei of radioactive sample to decay (activity of source of radiation to fall to half its starting level)

• Time it takes for # atoms in sample to halve

• Integrated form of first-order rate law in which N is substituted for concentration of X

http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/interface.swf?chapter=chapter_02&folder=half_life

04/10/23 23

Generic Half-Life Chart Time     Amount Remaining     Amount Decayed

0 100% 0%

1 half-life 50% 50%

2 half-lives 25% 75%

3 half-lives 12.5% 87.5%

04/10/23 24

• The half-life of 23994Pu is 2.411 x 104 years.

How many years will elapse before 99.9% of a given sample decomposes?– We have no specific amounts. However, we do

know that 0.999 of our original 1.000 decomposes, leaving 0.001 remaining. We can thus establish the ratio N/N0 as 0.001/1.000. We can find k from t1/2.

– k = 0.693/ t1/2 = 0.693/ 2.411 x 104 yr = 2.87 x 10-

5/yr– ln [N/N0] = -kt = ln(0.001) = 2.87 x 10-5/yr– t = 2.87 x 105 yr– Total time is about 10 half-lives. We should have

about 1/210 (or 0.001) of our original material remaining, and we do.

04/10/23 25

• The half-life of protactinium-217 is 4.9 x 10-3 s. How much of a 3.50 mg sample of 217

91Pa will remain after 1.000 sec?# half-lives = 1 half-life x 1.000s = 204

4.9 x 10-3 s

• ½204 = 3.9 x 10-62

• 3.50 (3.9 x 10-62) = 1.4 x 10-61 mg• Because of the short half-live,

essentially none of original nuclide remains after one second.

04/10/23 26

Homework:

Read 18.2-18.3, pp. 883-889

Q pp. 907-908, #19, 20, 23, 26, 28

04/10/23 27

Aging carbon-containing materials

• 14C is not natural isotope– Constantly formed in upper atmosphere– 14N is bombarded w/neutrons, keeping proportion of 14C

relatively constant• When alive, plants/animals maintain same proportion of

14C in bodies because C continuously recycled• When organism dies

– 14C no longer replenished by diet– Fraction of isotope in dead organic matter decreases with time

• By comparing living/ancient 14C and comparing them– Reliably determine ages of biological materials that range from

1700 to 17,000 years old (half-life of C-14 is 5730 years)• Rule of thumb for radioactive isotope dating of materials

– Age of sample should be 0.3 - 3 half-lives of isotope used for dating

04/10/23 28

04/10/23 29

• A sample of bone taken from an archeological dig was determined by radiocarbon dating to be 12,000 years old. If we assume that a constant atmospheric C-14/C-12 ratio has 13.6 disintegrations per minute per gram of carbon, how many disintegrations per minute per gram does our 12,000 year old sample give off (half-life for carbon-14 = 5730 year)?

• k = 0.693/t1/2 = 0.693/5730 yr = 1.21 x 10-4/yr.

• ln(N/N0) = -kt = (- 1.21 x 10-4/yr)(12,000 yr) = -1.45

• N/N0 = e-1.45 = 0.234

• N0 = 13.6 disintegrations, so N = 0.234(13.6)

• N = 3.2 disintegrations per minute per gram

• If we start w/1.000 g of strontium-90, 0.953 g will remain after 2.00 yr.

• What is the half-life of strontium-90?– k = -1/t ln Nt/NO

– = -1/2.00 yr ln 0.953g/1.000g

– k = -1/2.00 yr (-0.0481) = 0.0241 yr-1

– T1/2 = 0.693/k = 0.693/0.0241 yr-1 = 28.8 yr

• How much strontium-90 will remain after 5.00 yr?– ln Nt/NO = -kt = (0.0241 yr-1)(5.00 yr) = -0.120

– Nt/NO = e-0.120 = 0.887 g (ev or INV LN function of calculator)

– Nt = (0.887)NO = (0.887)(1g) = 0.887 g

• What is the initial activity of the sample in Bq and in Ci?– k = (0.0241/yr)(1 yr/365 days)(1 day/24 hr)(1 hr/3600 s) = 7.64 x 10-10 s-1

– (1.000 g Sr-90)(1 mol Sr-90/90 g Sr-90)(6.022 x 1023 atoms Sr/1 mole Sr-90) = 6.7 x 1021 atoms

– Total disintegrations/s = (7.64 x 10-10 disintegrations/atom - s)(6.7 x 1021 atoms ) = 5.1 x 1012 disintegrations/s = same as Bq

– (5.1 x 1012 disintegrations/s)(1 Ci/ = 3.7 x 1010 disintegrations/s) = 1.4 x 102 Ci04/10/23 30

04/10/23 31

Most devices for detecting radioactivity depend on formation of ions

• Darkening of photographic plates, discharging of electroscopes, and damage to biological tissue all involve ionization

• Geiger counter (Geiger-Müller tube) – Particle-produced ions trigger electricity pulse that is counted– Beta/gamma radiation

• Cloud chambers– Measure charged particles (including alpha/beta particles)

• Scintillation counters– Measure many different types– Flashes produced counted as measure of # particles emitted

• Film dosimeters– Film reveals whether worker exposed to excess radiation– Gives total dose of radiation received

04/10/23 32

Nuclear energy

• One important consequences of Einstein's theory of relativity was discovery of equivalence of mass and energy

• Total energy content (E) of system of mass, m is given by Einstein's theory

– E = mc2 where c is velocity of light (3.0 x 108 m/s)

• Nuclear energies expressed in electronvolt (eV) and megaelectronvolt (MeV = 106 eV)

– 1 eV = 1.602 x 10-19 J; 1 MeV = 1.602 x 10-13 J– 1 u (atomic mass unit of mass) = 1.661 x 10-27 kg =

931.5 MeV of energy

04/10/23 33

• Mass of nucleus is direct measure of its energy content

• Atomic mass of He is 4.002603 u  – Add up mass of P/N/E

• There is difference of 0.030377 u • All atoms are lighter than sum of masses of

protons (1.007825 g), electrons, and neutrons (1.008665 g)

• Mass defect, Δm, equal to total mass of products minus total mass of reactants (difference between total mass of nucleons and measured mass of nucleus itself)– Reflects stability of nucleus

04/10/23 34

– To extract proton/neutron from nucleus, we have to pull pretty hard  • Find that it will regain missing mass• Binding energy defined as energy

released when nucleus is assembled from its constituent nucleons

–Equal to energy needed to tear nucleus apart into its nucleons (so mass defect same as binding energy)

–Literally energy that binds together N/P in nucleus

– So with our helium atom, missing 0.030377 u released when nucleons come together• That energy has to be put back to split

nucleus up again

04/10/23 35

• Binding energy measures difference between stability of products of reaction and starting materials– Provides quantitative measure of nuclear

stability– Larger the binding energy (more negative),

more stable nucleus is toward decomposition

– Average binding energy per nucleon-binding energy of nucleus divided by mass number

– Larger binding energy per nucleon, more stable nucleus is

• Calculate the mass change for decay of mole of U-238.– 238

92U 23490

Th + 42He

– 233.9942 g + 4.0015 g – 238.0003 g = -0.0046 g– ΔE = Δ(mc2) = c2Δm– (3.00 x 108 m/s) 2(-0.0046 g)(1kd/1000g)– -4.1 x 1011 kg-m2/s2 = -4.1 x 1011 J– Notice Δm converted to kg (SI unit of mass) to

obtain ΔE in joules (SI unit for energy)– Negative sign indicates energy is released in

reaction (over 400 billion joules/mole of U)

04/10/23 36

04/10/23 37

• Determine the binding energy in J/mol and MeV/nucleon for 101

46Pd (atomic mass = 100.908287 g/mol).

• Mass of individual nucleons46 x 1.007825 g/proton = 46.35995 g55 x 1.009665 g/neutron = 55.476575 g 101.836525 g/mol• mass defect = 101.836525 g – 100.908287

g = 0.928238 g• ∆E = ∆mc2 = -9.28238 x 10-4 kg (3.00 x 108

m/s)2 (minus sign because mass is lost in forming the nuclide) ∆E = -8.35 x 1013 J/mol

-8.35 x 1013 J 1 MeV 1 mol 1 nuclide = -8.59 MeV mol 1.60 x 10-13 J 6.02 x 1023 nuclides 101 nucleons nucleon

04/10/23 38

Natural Radioactivity• Few naturally occurring radioactive isotopes

– K-40 decays into Ar-40, found in air– C-14 determines age of artifacts– Vanadium-50, Tritium (H-3), radon, thorium, lanthanuim-138

• Polonium, Z=84 to uranium, Z=92– Radon-222 forms from decomposition of U in rocks (granite)

• Gathers in lower, unventilated areas of houses• Gas decomposes into solid polonium, which if decays in lungs, emits

alpha particles which can cause cancer

– Radium-226-causes biological damage– U-238 used to determine age of very old rocks as it decays to

lead-206

• Transuranium elements (93-118) artificially prepared/radioactive

04/10/23 39

• Used depending on properties of particular isotope

– Tracers to uncover how certain chemical reactions occur

• Phosphorus-32 shows details of how plants use P to grow/reproduce

– Medical applications (radioactivity/short half-life necessary to ensure rapid decay and elimination from body)

• Diagnostics (PET scan)• Treatment (I-131 for thyroid cancer)

– Determine age of various artifacts (C-14)– Smoke detectors (Americium-241)– Food irradiation (gamma rays)– Irradiation in pest control

04/10/23 40

Artificial Radioactivity• Artificial radioactivity results when unstable

nucleus produced by transmutation• Nuclear transmutation-process of converting one

element into another– Al atoms bombarded w/alpha particles produces

radioactive P-30• P-30 decays by positron emission and has half-life

of 2.5 min• Does not occur naturally in phosphorus

compounds

04/10/23 41

• Induced transmutation– Neutrons easily captured by stable nuclei

• No charge• Not repelled by target nuclei• No KE needed to overcome electrostatic

repulsion if protons/alpha particles used

– Readily produce "artificial" radioactivity– New nucleus formed has higher n : p ratio– Leads to product that decays by beta

decay– Neutron capture by chlorine-37 yields

chlorine-38

04/10/23 42

• Nuclear transmutation processes are abbreviated using

– Target nucleus (bombarding particle, ejected particle)

– Product nucleus– n, p, d, α, e, and γ used to represent neutron,

proton, deuteron, alpha particle, electron, and gamma ray

04/10/23 43

Nuclear Fission-any process that yields two nuclei of almost equivalent mass

• Does not occur spontaneously– Requires bombardment of fissile nucleus (235

92U or 23994Pu)

– By energetic neutrons– That causes release of several more neutrons

• Chain reaction– Neutrons released in each fission start additional fissions– Two ways to keep fission from becoming uncontrolled

• Small enough sample so released neutrons will not hit other U-235 nuclei to continue chain reaction– Critical mass of several pounds needed before chain

reaction will be sustained (explosion)• Excess neutrons can be absorbed by certain materials

(graphite, paraffin)– Control rods adjust number of available neutrons and

rate of nuclear reactions

04/10/23 44

• Fission reactors-employs controlled chain reaction to provide continuous source of useful energy

– Containment shell of concrete/steel for shielding– Fuel rods in core as source of energy (enriched U-235)– Moderator creates neutrons for reaction – Control rods regulate rate of fission (cadmium)– Coolant (water/liquid Na) removes thermal energy from

core– Heat exchanger receives thermal energy and produces

steam for generation of electrical energy by turbine connected to reactor

– Problems• Heat causes thermal pollution• Radioactive waste disposal

– Benefits• Energy• Produce radioactive isotopes

04/10/23 45

Nuclear Fusion-combination of two nuclei to form a larger, more stable nucleus

• For self-sustaining fusion reaction to occur– Temperatures of 40,000,000 K needed– Nucleus has higher average binding energy per

nucleon– Because all nuclei positively charged, they must

collide with enormous force to combine • At these temperatures, gases completely ionized into

mixture of positive nuclei and electrons (plasma)

• One gram of hydrogen upon fusion releases energy equivalent to combustion of 20 tons of coal

– Fusion of four moles of H atoms releases 2.6 x 109 kJ of energy

+ 2γ + 2ν (neutrino)

04/10/23 46

Interaction of radiation with matter

• Alpha/beta/gamma rays pass through matter– Alpha/beta particles colliding with electrons

• Lose small fraction of their energy in collision

– Forcefully eject electrons from atoms/ molecules

• Because alpha/beta particles extremely energetic, thousands of collisions required to bring them to rest

– Produce ions• Particles produce "tracks" of ionization• Alpha/beta/gamma rays known as ionizing

radiation

04/10/23 47

Units of Radiation Dose-rad and rem

• Rad (radiation absorbed dose) – 0.01 joule of energy absorbed per kilogram

• Beams of different radiations cause very different biological damage even when body absorbs same amount of energy from each type, it is necessary to define unit specifically for biological tissue

– rem (radiation equivalent in man)• Absorbed dose in rads x relative biological

effectiveness factor, RBE– dose (in rem) = RBE x dose (in rad)– For beta and gamma rays RBE = 1.0; for fast

neutrons and alpha particles RBE = 10• Dose of one rad of alpha radiation = 10 rem

04/10/23 48

Homework:Read 18.4-18.7, pp. 889-903Q pp. 908-909, #33, 34, 38, 44Do 1 additional exercise and 1 challenge problemSubmit the quizzes by email to me:http://www.cengage.com/chemistry/book_content/

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http://www.cengage.com/chemistry/book_content/0547125321_zumdahl/ace/launch_ace.html?folder_path=/chemistry/book_content/0547125321_zumdahl/ace&layer=act&src=ch18_ace3.xml