chapter 21: nuclear chemistry chemistry: the molecular nature of matter, 6e jespersen/brady/hyslop

Chapter 21: Nuclear Chemistry

Chemistry: The Molecular Nature of Matter, 6E

Jespersen/Brady/Hyslop

Jespersen/Brady/Hyslop Chemistry: The Molecular Nature of Matter, 6E

2

How are atoms formed? Big Bang—Intense heat ~109 K

Cooled quickly to 106 K—T of stars e–, p, n formed and joined into nuclei—atoms

Mostly H and He (as in our sun) Rest of elements formed by nuclear

reactions Fusion—two nuclei come together to

form another heavier nucleus Fission—one heavier nucleus splits into

lighter nuclei

Various other types of reactions+

+


3

Nuclear Shorthand Nucleons

Subatomic particles found in the nucleus Protons (p) Neutrons (n)

Nuclide Specific nucleus with given atomic number

(Z ) Atomic Number (Z )

Number of protons in nucleus Determines chemical properties of nuclide Z = p

Mass Number (A)—mass of nuclide A = n + p


4

Shorthand for Writing Nuclides Where X = atomic symbol

e.g. In the neutral atom: e– = p = Z Isotopes

Nuclides with same Z (same number of p), but different A (different n)

Hydrogen Deuterium Tritium

1 p 1 p + 1 n 1 p + 2 n


5

Radioactivity Radioactive isotopes

Isotopes with unstable atomic nuclei Emit high energy streams of particles or

electromagnetic radiation Radionuclides

Another name for radioactive isotopes Undergo nuclear reactions

Uses Dating of rocks and ancient artifacts Diagnosis and treatment of disease Source of energy


6

Mass Not Always Constant Mass of particle not constant under all

circumstances It depends on velocity of particle relative to

observer As approaches speed of light, mass increases

When v goes to zero Particle has no velocity relative to observer v/c 0 Denominator 1 and m = mo

2)/(1 cv

mm

m = mass of particle

v = velocity of particlem = rest massc = speed of light


7

Why don’t we observe mass change?

In lab and ordinary life, velocity of particle is small

Only see mass vary with speed as velocity approaches speed of light, c As v c, (v/c) 0 and m ∞

In lab, m = mo within experimental error Difference in mass too small to measure

directly Scientists began to see relationship

between mass and total energy Analogous to potential and kinetic energies


8

Law of Conservation of Mass and Energy

Mass and energy can neither be created nor destroyed, but can be converted from one to the other.

Sum of all energy in universe and all mass (expressed in energy equivalents) in universe is constant

Einstein Equation E = (mo)c

2

Where c = 2.9979 × 108 m/s


9

Mass Defect Rest mass of nuclide is always less than sum of

masses of all individual nucleons (neutrons and protons) in that same nuclide Mass is lost upon binding of neutrons and protons

into nucleus When nucleons come together, loss of mass

translates into release of enormous amount of energy by Einstein's relationEnergy released = – Nuclear Binding

Energy Nuclear Binding Energy

Amount of energy must put in to break apart nucleus


10

What is Mass Loss?

nucleonsnucleus mmm

For given isotope of given Z and A

or


11

Ex. 1 Binding Energy CalculationWhat is the binding energy of 7Li3+ nucleus?

Step 1. Determine mass loss or mass defectA. Determine mass of nucleus

mass of 7Li3+ = m (7Li isotope) – 3me

= 7.016003 u – 3(0.0005485 u) = 7.0143573 u

B. Determine mass of nucleonsmass of nucleons = 3 mp + 4 mn

= 3(1.007276470 u) + 4(1.008664904 u) = 7.056489026 u


12

Ex. 1 Binding Energy Calculation (cont.)C. m = mnucleus – mnucleons

= 7.0143573 u – 7.056489026 u= –0.0421317 u= mass lost by nucleons when they form

nucleusStep 2. Determine energy liberated by this

change in massE = (mo)c2

E = – 6.287817 × 10–12 J/atom


13

Ex. 1 Binding Energy Calculation (cont.)

E = –6.287817 × 1012 J/atom × 6.0221367 x 1023

atoms/moleE = –3.78655 × 1012 J/mole = –3.78655 × 109 kJ/mole

Compare this to: 104 – 105 J/mol (102 – 103 kJ/mol) for

chemical reactions Nuclear ~ 1 – 10 million times larger

than chemical reactions!!


14

MeV (Energy Unit)

Nuclear scientists find it convenient to use a different Energy unit: MeV (per atom)

Electron volt (eV) Energy required to move e across energy

potential of 1 V 1 eV = 1.602 × 10–19 J M(mega) = 1 × 106 So 1 MeV = 1 × 106 eV 1 MeV = 1.602 × 10–13 J


15

Ex. 1 Binding Energy Calculation in MeV

For Ex. 1. Converting E to MeV gives

Often wish to express binding energy per nucleon so we can compare to other nuclei For Li3+ with 3 1p and 4 n this would be


16

Ex. 2 Calculate E Released

The overall reaction in the sun responsible for the energy it radiates is

How much energy is released by this

reaction in kJ/mole of He?

m (1H) = 1.00782 um (4He) = 4.00260 um (0+) = 0.00054858 u


17

Ex. 2 Calculate E Released (cont.) m = mproducts – mreactants

m = m (4He) + 2m (e +) – 4m (1H)

m = 4.00260 u + 2(0.00054858 u) – 4(1.00782 u)

m = –0.02758 u [We will convert u to kg, kg m2/s2 to J, and atoms to moles

in the following calculation]

E = –2.479 × 1012 J/mol = –8.268 × 109 kJ/mol


Your Turn!Determine the binding energy, in kJ/mol and MeV/atom, for an isotope that has a mass

defect of –0.025861 u.A. –2.3243 × 109 kJ/mol; 24.092

MeV/atomB. –3.8595 × 10–12 kJ/mol; 24.092

MeV/atomC. –7.7529 kJ/mol; 8.03620 × 10–8

MeV/atomD. –2.3243 × 109 kJ/mol; 4.1508 × 10–2

MeV/atom18


Your Turn! - Solution

19


20

Divide binding energy EB by mass number, EB/A

Get binding energy per nucleon

Binding Energies per Nucleon


21

Implications of Curve Most EB /A in range of 6 – 9 MeV (per

nucleon) Large binding energy EB /A means stable

nucleus Maximum at A = 56

56Fe largest known EB /A Most thermodynamically stable Nuclear mass number (A) and overall charge

are conserved in nuclear reactions Lighter elements undergo fusion to form

more stable nuclei


22

Implications of CurveFusion

Researchers are currently working to get fusion to occur in lab

Heavier elements undergo fission to form more stable elements

Fission

Reactions currently used in bombs and power plants (238U and 239Pu)

As stars burn out, they form elements in center of periodic table around 56Fe


23

Radioactivity Spontaneous emission of high energy

particles from unstable nuclei Spontaneous emission of fundamental

particle or light Nuclei falls apart without any external stimuli

Discovered by Becquerel (1896) Extensively studied by Marie Curie and

her husband Pierre (1898 early 1920's) Initially worked with Becquerel


24

Fun Facts Marie and Pierre Curie discovered

polonium and radium Nobel Prize in Physics 1903

For discovery of Radioactivity Becquerel, Marie and Pierre Curie—all three

shared Nobel Prize in Chemistry 1911

For discovery of Radium and its properties Marie Curie only

Marie Curie - first person to receive two Nobel Prizes and in different fields


25

Discovery of Radioactivity

Initially able to observe three types of decay

Labeled them , , rays (after first three letters of Greek alphabet)

If they pass through an electric field, very different behavior


26

Discovery of Radioactivity rays attracted to

negative pole so its positively charged

rays attracted to positive pole so its negatively charged

rays not attracted to either so its not charged


27

Nuclear Equations Used to symbolize decay of nucleuse.g. 238U 234Th + parent daughter Produce new nuclei so need separate

rules to balanceBalancing Nuclear Equationsa. Sum of mass numbers (A, top) must be

same on each side of arrowb. Sum of atomic numbers (Z, bottom) must

be same on each side of arrow

He4292 90


28

Types of Spontaneous Emission 1. Alpha () Emission

He nucleus2 n + 2 p A = 4 and Z = 2

Daughter nuclei has:A decreases by 4 A = – 4

Z decreases by 2 Z = – 2Very common mode of decay if Z > 83 (large radioactive nuclides)Most massive particle

e.g.


Balancing Nuclear Equations

29

1. The sum of the mass numbers (A; the superscripts) on each side of the arrow must be the same

2. The sum of the atomic numbers (Z; the subscripts; nuclear charge) on each side of the arrow must be the same

e.g.

A: 234 = 230 + 4Z: 92 = 90 + 2


Emission of electrons Mass number A = 0 and charge Z = –1 But How? No electrons in nucleus! If nucleus neutron rich — nuclide is too

heavy

2. Beta (– or e–) Emission

30


2. Beta (– or e–) Emission

31

Charge conserved, but not mass m E

Ejected e– has very high KE + emits Antineutrino variable energy particle Accounts for extra E generated

e.g.


3. Gamma () Emission Emission of high energy photons Often accompanies or emission Occurs when daughter nucleus of some

process is left in excited state Use * to denote excited state

Nuclei have energy levels analogous to those of e– in atoms

Spacing of nuclear E levels much larger light emitted as -rayse.g.

32


4. Positron (+ or e+) Emission

Emission of e+

Positive electron Where does + come from?

If nucleus is neutron poor) Nuclide too light

Balanced for charge, but NOT for mass

33


4. Positron (+ or e+) Emission Product side has much greater mass! Reaction costs energy Emission of neutrino

Variable energy particle Equivalent of antineutrino but in realm of

antimatter e+ emission only occurs if daughter

nucleus is MUCH more stable than parent

34


4. Positron (+or e+) EmissionWhat happens to e+? Collides with electron to give matter

anti-matter annihilation and two high energy -ray photons m E

Annihilation radiation photons Each with E = 511 keV

What is antimatter? Particle that has counterpart among

ordinary matter, but of opposite charge

High energy light, massless Detect by characteristic peak in

-ray spectrum

35


5. Electron Capture (EC) e– in 1s orbital

Lowest Energy e– Small probability that e– is

near nucleus e– actually passes through

nucleus occasionally If it does:

Net effect same as e+ emission

36


37

Types of Spontaneous Emission

6. Neutron Emission = ( ) Fairly rare Occurs in neutron rich nuclides Does not lead to isotope of different

element

7. Proton Emission = ( ) Very rare

n10

p11


38

Types of Spontaneous Emission

8. Spontaneous Fission No stable nuclei with Z > 83 Several of largest nuclei simply fall

apart into smaller fragments Not just one outcome, usually several

different—see distribution

Fm256100 SbIn 131

5112549

IAg 13653

12047


39

Summary—Common Processes1. Alpha () Emission

Very common if Z > 83

2. Beta () Emission e–

Common for neutron-rich nuclides—below belt of stability

3. Positron (+) Emission e+

Common for neutron-poor nuclides—above belt of stability

4. Electron Capture (EC) Occurs in neutron-poor nuclides, especially if Z > 40

5. Gamma () Emission Occurs in metastable nuclei (in nuclear excited

state)


40

Learning Check Complete the following table which refers

to possible nuclear reactions of a nuclide:

Emission Z = p

n e A New Element?

–

+

EC

–2 –2 0 –4 yes

+1+1–1 0 yes

+1 –1 0 yes–1

0 0 0 0 no

+1+1–1 0 yes


41

Learning CheckBalance each of the following equations

a.

b.

c.

d.

e.


Your Turn!What is the missing species, , in the

following nuclear reaction?

A.B.C.D.

42

23994Pu

24798Cf

23895Am

23894Pu


43

What Holds Nucleus Together? Consider nucleus

Neutrons and protons in close proximity Strong proton-proton repulsions Neutrons spread protons apart Neutron to proton ratio increases as Z

increases

Strong Forces Force of attraction between nucleons Holds nuclei together Overcomes electrostatic repulsions

between protons Binds protons and neutrons into nucleus


44

Table of Nuclides Chart where Rows = different atomic

numberColumns = different number of neutrons

Symbol entered if element is known Stable nuclei

Natural abundance entered below symbol Shaded area Trend of stable nuclei = Belt of Stability Z ≈ number of neutrons (for elements 1 to 20)

Unstable nuclei Give type(s) of radioactive decay

(spontaneous) Outer edges, most of atoms


45

Table of Nuclides

Atomic number (Z = number of protons)

Num

ber

of

neu

trons


46

Table of Nuclides

Shaded area = stable nuclei Trend of stable nuclei = diagonal line

= Belt of Stability Z ≈ number of neutrons (for

elements 1 to 20) Note: only a small corner of table is

shown. (The complete is in Handbook of Chemistry and Physics)


47

Belt of Stability Each isotope is a dot Up to Z = 20

Ratio n /Z = 1 As Z increases, n >

Z and By Z = 82, n/Z ~1.5

n = number of neutrons

Z = number of protons

n

Z = p

1n:1p

Stable nuclide, natural Unstable nuclide, natural Unstable nuclide, synthetic

Band of Stability

1n:1p

1.1n:1p

1.2n:1p

1.3n:1p

1.4n:1p

1.5n:1p

e– emitters

e+ emitters


48

How To Predict if Nuclei are Stable1) Atomic Mass = weighted average of masses of

naturally occurring isotopes, i.e. most stable ones2) Compare atomic mass of element to A (atomic mass

number) of given isotope and see if it is more or less Atomic Mass > A too light to be stable Atomic Mass < A too heavy to be stable

Ex. Atomic Mass

Conclusion

180Os 135I Final note: All nuclei with Z > 83 are radioactive

190.2

126.9

Too light, neutron poor

Too heavy, neutron rich


49

More Patterns of Stability If we look at stable and unstable nuclei, other

patterns emerge 283 stable nuclides (out of several thousand

known nuclides) If we look at which have even and odd numbers of

protons (Z) and neutrons (n); patterns emerge

Z n # stable nuclides

even

even

165

even

odd 56

odd even

53

odd odd 5

2H, 6Li, 10B, 14N, 138La


50

More Patterns of Stability Clearly NOT random: even must imply

greater stability Not too surprising

Same is true of electrons in molecules Most molecules have an even number of

electrons, as electrons pair up in orbitals Odd electron molecules, radicals, are

very unstable, i.e. very reactive!!


51

Magic Numbers Look at binding energies, see certain

numbers of protons and neutrons result in special stability

Called Magic Numbers 1n and 1p in separate shells Magic numbers (for both 1n and 1p)

are 2, 8, 20, 28, 50, 82, 126…

For e– pattern of stability is: 2, 10, 18, 36, 54, 86…(Noble gases)


52

Magic Numbers Special stability of noble gases due

to closed shells of occupied orbitals Structure of nucleus can also be

understood in terms of shell structure With filled shells of neutrons and

protons having added stability At some point adding more neutrons

to higher energy neutron shells decreases stability of nuclei with too high a neutron to proton ratio


Your Turn!Isotopes above the band of stability are

morelikely to:A. emit alpha particlesB. emit gamma raysC. capture electronsD. emit beta particles

53


54

Radioactive Nuclei Found in Nature Non-naturally occurring elements (man-made

unstable) are denoted by having atomic mass in parentheses

All nuclei with Z > 83 are radioactive Yet some elements with Z between 83 and 92

occur naturally Atomic weight is NOT in parentheses

How can this be? There are three heavy nuclei, which have very

long half-lives Long enough to have survived for billions of years

Each parent of natural decay chain


55

Decay Chains238U half-life (½) = 4.5 billion years emitter Daughter 234Th is also radioactive

– emitter Half-life much shorter

Long sequence of emissions, and – Recall that emission changes A by 4, while

– emission A = 0 Result: every member of chain has

A = (4n + 2) where n = some simple integer


56

238Uranium Decay Chain238U 234Th

5109 y

25 d

, 234Pa

7 hr

, 234U

5.7105 y

230Th,

8104 y226Ra

, 2103 y

222Rn

4 d218Po

3 m214Pb

,

27 m214Bi

20 m

, 214Po

1.610–4 s

210Pb

22 y,

210Bi

5 d210Po

138 d206Pb

92 90 91 92

90888684

82 83 84 82

82 84 83

A stable isotope


57


58

Decay Chains Final stable member of sequence is 206Pb Some intermediate nuclides have

reasonably short half-lives Still found in nature because they are

constantly being replenished by decay of nuclei further up chain

Uranium-containing minerals (pitchblende is most famous) contain many radioactive elements


Your Turn!When the reaction, ,

occurs, the particle emitted is:A. an alpha particleB. a beta particleC. an electronD. a gamma ray

59


60

Transmutation Change of one isotope for another Caused by

1. Radioactive decay 2. Bombardment of nuclei with high energy

particles particles from natural emitters Neutrons from atomic reactors Protons made by stripping electrons for hydrogen

Protons and particles can be accelerated in electrical field to give higher E

Mass and energy of bombarding particle enter target nucleus to form compound nucleus


61

Non-Spontaneous Nuclear Processes

Fusion Occurs in stars—right now How elements formed

Induced Fission Bombard heavy nuclei with neutron


62

Compound Nucleus Designated with * High energy due to velocity of incoming

particle Energy quickly redistributed among nucleons,

but usually unstable To get rid of excess energy, nucleus ejects

something Neutron ▪ Proton Electron ▪ Gamma radiation

Decay leaves new nucleus different from original


63

Example: Transmutation

p11

178

189

147

42 O F N He

Compound nucleus

New nucleus

Target nucleus

Bombard-ing particle

High energy particle


64

Transmutation Can synthesize given nucleus in many

ways:

Once formed, compound nucleus has no memory of how it was made

Only knows how much energy it has

Al Na He 2713

2311

42

Al Mg 2713

2612

11

p

Al Mg H 2713

2512

21


65

TransmutationDecay pathway depends on how much energy 0

02713 Al

p112612 Mg

n102613 Al

pn 11

10

2512 Mg

He Na 42

2311

Al 2713


66

Transmutation Used to synthesize new isotopes

> 900 total Most not on band of stability

All elements above 93 (neptunium) are man- made Includes actinides above 93 + 104 – 112 +

114 Heavier elements made by colliding two

larger nuclei Also known as fusion n1

0269110

270110

20882

6228 Ds Ds Pb Ni


Your Turn!What would be the element produced

from the fusion of with ? The species

would be in a high energy state and in time

would undergo decay to other species.A. NoB. LrC. UD. Hs

67

5927Co 192

76Os


68

Measuring Radioactive Decay Atomic radiation = ionizing radiation

Creates ions by knocking off electrons Geiger Counter

Consists of a tube with a mica window, low pressure argon fill gas and two high voltage electrodes

Detects and radiation with enough E to penetrate mica window

Inside tube, gas at low pressure is ionized when radiation enters

Ions allow current to flow between electrodes Amount of current relates to amount of radiation


69

Measuring Radioactive Decay Scintillation Counter

Surface covered with chemical Emits tiny flash of light when hit by radiation Emission magnified electronically and counted

Film Dosimeters Piece of photographic film Darkens when exposed to radiation How dark depends on how much radiation

exposure over time Too much exposure, person using must be

reassigned to other work


70

Activity Number of disintegrations per second Used to characterize radioactive material A = kN

k = first order decay constant in terms of number of nuclei rate than concentration

N = number of radioactive nuclides

Law of radioactive decay Radioactive decay is first order kinetics

process


71

Units of Activity SI unit

Bequerel (Bq) 1 disintegration per second (dps) 1 liter of air has ~ 0.04 Bq due to 14C in

CO2

Older unit Curie (Ci)

3.7 × 1010 dps = 3.7 × 1010 Bq Activity in 1.0 g 226Ra = 1 Ci


72

Half-Life Time it takes for number of nuclides, Nt ,

present at time, t, to fall to half of its value.

Half-lives are used to characterize nuclides If you know half-life:

Can use to compute k Can also calculate A of known mass of

radioisotope

kkt

693.02ln2

1


73

Ex. 3 Activity of Sr-90What is the activity of 1.0 g of strontium-90? The half-life = 28.1 yearsStep 1. Convert t½ to seconds

Step 2. Convert t½ to k


74

Ex. 3 Activity of Sr-90 (cont.)Step 3. Convert mass of 90Sr to number

of atoms (N)

Step 4. Calculate Activity = kN

A = 5.23 1012 atoms Sr/s 1 disintegration/atomA = 5.23 1012 dps or 5.23 1012 Bq


75

Ex. 4 Mass of 3H in Sample3H, tritium, is a emitter with a half-lifet½ = 12.26 yrs. MW = 3.016 g/mol. How many grams of 3H are in a 0.5 mCi sample?Step 1. Convert half-life to seconds as Ci is in disintegrations per second (dps)

Step 2. Convert t½ to k


76

Ex. 4 Mass of 3H in Sample (cont.)Step 3. Convert Ci to dps

Step 4. Calculate g 3H to get this activity

Step 5. Convert atoms to g

= 5.2 × 10–8 g


77

Exposure Units Not all materials equally absorb radiation,

thus activity doesn’t describe effect of exposure 1 gray (Gy) = 1 J absorbed energy/kg material

SI unit of absorbed radiation 1 rad = absorption of 10−2 J/ kilogram of tissue

Older unit 1 Gy = 100 rad

These units don’t take into account type of radiation


78

Exposure UnitsSieverts (Sv)

SI unit of dose equivalent, H Depends on amount and type of radiation

as well as type of tissue absorbing it H=DQN

H = dose in Sv D = dose in Gy Q = radiation properties N = other factors

Rem = older unit 1 Rem = 10–2 Sv Still used in medicine


79

Exposure to Radiation Typically X ray = 0.007 rem or 7 mrem 0.3 rem/week is maximum safe exposure

set by US government 25 rem (0.25 Sv): Causes noticeable changes

in human blood 100 rem (1 Sv):

Radiation sickness starts to develop 200 rem (2 Sv):

Severe radiation sickness 400 rem (4 Sv):

50% die in 60 days Level of exposure or workers at Chernobyl when

steam explosion tore apart reactor 600 rem (6 Sv): lethal dose to any human


Your Turn!Workers cleaning up the Fukushima reactors were exposed to as much as 400 mSv units of radiation per hour. How many rems of exposure does this correspond to?A. 4000 remB. 400 remC. 40 remD. 4 rem

80

100 mrem 1 rem400 mSv 40 rem

mSv 1000 mrem


81

Why is Radiation Harmful? Not heat energy

Ability of ionizing radiation to form unstable ions or neutral species with odd (unpaired) electrons

Free radicals Chemically very reactive Can set off other reactions Do great damage in cell

H O H+ +H+ O H

H O Hradiation

H O H+

+ 0e-1


82

Which Types are Most Harmful? High energy gamma () radiation and X

rays Massless High velocity Penetrate everything but very dense

materials, such as lead

Which type is least harmful? Alpha () particles

Most massive Quickly slow after leaving nucleus Don’t penetrate skin


83

Background Radiation Presence of natural radionuclides means we

can’t escape exposure to some background radiation Cosmic rays (from sun) hit earth

Turn 14N 13C 13C emits – particles Incorporated into food chain from CO2 via

photosynthesis Radiation from soil and building stone

From radionuclides native to Earth’s crust Top 40 cm of soil hold 1 g radium ( emmiter) /sq

kilometer 40K emit – particles

Total average exposure 360 mrem/year 82% natural radiation 18% man made


84

Radiation Intensity Intensity of radiation varies with

distance from the source Farther from emitter, lower intensity of

exposure Relationship is governed by Inverse

Square Law, where: I is intensity and d is distance from source


85

Ex. 5 Inverse Square LawIf the activity of a sample is 10 units at 5 meters from the source, what is it at 10 m?

What distance is needed to reduce 1 unit at 1 yd to the 0.05 units?


Your Turn!How far away from a radioactive source producing 40 rem/hr at a distance of 10 m would you need to be to reduce your exposure to 0.4 rem/hr?

A. 32 mB. 100 mC. 200 mD. 1000 m

86

2

2

40 rem 10 m100 m

0.4 remd


87

Radioactive Decay—Kinetics Spontaneous decay of any nuclide

follows first order kinetics May be complicated by decay of daughter

nuclide For now consider single step decay

processes Rate of reaction for first order process

A products In nuclear reaction, consider rate based on

number of nuclei N present


88

Radioactive Decay—Kinetics The integrated form is:

ln N – ln No = – kt N = number of nuclei present

at time t No = number of nuclei present

at t = 0

Plot ln N (y axis) versus t (x axis)

Yields straight line—indicative of first order kinetics

Plot of N vs. time gives an exponential decay.

ln N

t

t

Nkt

oeNN


89

Ex. 6 Activity Calculations131I is used as a metabolic tracer in hospitals. It has a half-life, t½ = 8.07 days. How long before the activity falls to 1% of the initial value?

ktoeNN

t = 53.6 days


Your Turn!How many hours will it take a radioisotope

with a half-life of 10.0 hours to drop to 12.5% of its original activity?A. 30.0 hrsB. 20.0 hrsC. 40.0 hrsD. 63.2 hrs

12.5% of original activity is 3 half-lives or 30.0 hrs.

90


91

Radioisotope Dating How old is an object?

Fields — Geology, Archeology, and Anthropology

Nature provides us with natural clocks or stopwatches

A) Radiocarbon Dating (Willard Libby—Nobel Prize in 1960)

Cosmic rays (from space) enter atmosphere

Some react with N in atmosphere forming radioisotope 14C

– emitter with t½ = 5730 yr


92

14C Dating 14C becomes incorporated into

atmospheric CO2 in very small quantities 14C/12C ratio in air is slightly greater than

Earth’s crust because of ongoing enrichment Living organisms breath, eat, etc…

14C/12C equilibrate with atmosphere Radioactive 14C is uniformly distributed

around globe Tested experimentally Checked vs. counting tree rings, etc. For precise work, use correction based on

alternate methods


93

HOW? Freshly cut wood samples have ~15.3 cpm per gram of total carbon

cpm = counts per minute Ao = 15.3 cpm/g total C

Assumption: Ao was always 15.3 cpm, i.e. cosmic radiation is constant

When organism dies it stops eating, breathing, etc… 14C starts to decrease

14C Dating


94

Wooden implement in Egyptian tomb (~3000 BC) Have about half activity of fresh sample ~5000 years have elapsed

Method is applicable for objects Few hundred to ~20,000 years

Beyond this Activity of sample is very low Experimental uncertainties too big

This method used for dating1.Charcoal in cave paintings2.Linen wraps on Dead Sea scrolls

14C Dating


95

Ex. 7 C-14 DatingGeologists examine shells found in cliffs. Shells are CaCO3 and are made by living organisms. The activity of the shells is found to be 6.24 cpm/g total C. How old is the cliff formation?

21

2lnln

tt

ktAA

o

A = 6.24 cpm/g total CAo = 15.3 cpm/g total Ct½ = 5730 yr

Can use N/No and A/Ao interchangeably as A = kN

Since ratio, k cancels


96

Ex. 7 C-14 Dating (cont.)

Rearranging and solving for t

t = 7414 yr


97

B) Other Isotopes Provide Natural Clocks

Minerals (moon rocks) dated using isotopes with much longer half-lives

t½ = 1.27 × 109 yr

Compare ratios in rock

t½ = 4.5 × 109 yr

Rock with no other source of Pb can be dated using ratios


98

Ex. 8 Dating with UA sample of lava is found to contain 0.232 g of 206Pb and 1.605 g 238U. Since lead is volatile at the temperature of molten lava, all the 206Pb now present came from the decay of 238U, calculate the time since the solidification of this rock.Step 1. Mass of 238U that decayed =

= 0.268 g 238U decayed


99

Ex. 8 Dating with U (cont.) Step 2. Mass of 238U in lava initially (t =

0) No = 1.605 g + 0.268 g = 1.873 g

t = 1.0 × 109 yr


Your Turn!A wooden bowl fragment found at an old camp site thought to be approximately 11,000 years old was submitted for carbon-14 analysis. The sample was found to have 4.67 cpm/g total C. What is the

actual age of the sample?

A. 4260 yrsB. 3347 yrsC. 9810 yrsD. 2523 yrs

t = (5730 yrs × ln(4.67/15.3))/(ln 2) = 9810 yrs

100


101

Fission Induce by

bombarding unstable nucleus with a slow neutron

Nuclear chain reaction Neutrons generated

keep going

With small mass of 235U reaction continues, but easily controlled Some neutrons are

lost to environment


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Fission “Critical mass”

Too much 235U in one place

Too many neutrons absorbed

Too few lost Uncontrollable

fission Leads to explosion

Use control rods to absorb excess neutrons and keep reaction from going critical


103

Nuclear Reactor No chance of nuclear explosion

Critical mass requires pure 235U Reactor rods 2 – 4% 235U rest non-fissionable 238U

Core meltdown possible If heat of fission not carried away by cooling

water Or

Explosion possible High heat of fission splits H2O into H and O,

which recombine very exothermically and cause a chemical explosion

What happened at Chernobyl


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Nuclear Reactors Could it happen at U.S. reactors?

Extremely unlikely Chernobyl only single containment system U.S. has all double containment systems U.S. extra backup systems - both computer

and mechanical that would prevent


105

Nuclear Reactor

Use heat from nuclear reaction to heat steam turbine

Use to generate electricity


Your Turn!Which of the following fission reactions is Balanced?A.

B.

C.

D.

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Nuclear Fusion

Occurs when light nuclei join to form heavier nucleus

On a mass basis, fusion yields more than five times as much energy as fission

Source of the energy released in the explosion of a H-bomb The energy needed to trigger the fusion is

provided by the explosion of a fission bomb Source of energy in stars

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Thermonuclear Fusion Uses high temperatures to overcome

electrostatic repulsions between nuclei T required are >100 million °C Atoms want to fuse stripped of electrons

High initial energy cost Plasma

Electrically neutral, gaseous mixture of nuclei and electrons

Make plasma very dense (>200 g/cm–3) Brings nuclei within 2 fm = 2 × 10–15 m Pressures = several billion atm

Not there yet, major problem Containment of high temperature and pressures Magnetic field current approach

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chapter 21: nuclear chemistry chemistry: the molecular nature of matter, 6e jespersen/brady/hyslop

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