Chem 16 General Chemistry 1

13 Changes in the Nucleus

Dr. Gil C. Claudio

First Semester 2014-2015

Table of Contents

Contents

1 Radioactivity and Nuclear Equations 1

2 Patterns of Nuclear Stability 4

3 Nuclear Transmutations 6

4 Rates of Radioactive Decay 8

5 Detection of Radioactivity 10

6 Energetics of Nuclear Reactions 10

7 Nuclear Power: Fission 12

8 Nuclear Power: Fusion 13

9 Effect of Nuclear Radiation on Matter 13

ReferencesReferences of these notes

General Chemistry, 10th ed, by Ralph H. Petrucci, F. Geoffrey Herring,Jeffy D. Madura, and Carey Bisonnette.

Chemistry: The Central Science, 13th ed., by Theodore L. Brown, H. EugeneLeMay Jr., Bruce E. Bursten, Catherine J. Murphy, Patrick M. Woodward,and Matthew W. Stoltzfus.

Nuclear ChemistryNuclear chemistry is the study of nuclear reactions, with an emphasis on

their uses and their effects on biological systems.

energy and medical applications

used to help determine the mechanisms of chemical reactions, to tracethe movement of atoms in biological systems and the environment, andto date historical artifacts.

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1 Radioactivity and Nuclear Equations

Isotopes and NuclidesAtoms with the same atomic number but different mass numbers are

known as isotopes.

Themass number is the total number of nucleons in the nucleus.

Isotopes of the same element have different mass numbers, differentnatural abundances, and different stabilities.

E.g., the three naturally occurring isotopes of uranium are uranium-234(23492U, trace amounts), uranium-235 (

23592U, 0.7%), and uranium-238 (

23892U,

99.3%).

A nuclide is a nucleus containing a specified number of protons and neutrons.

Nuclides that are radioactive are called radionuclides, and atomscontaining these nuclei are called radioisotopes.

RadioactivityRadioactivity is a phenomenon in which small particles of matter ( or

particles) and/or electromagnetic radiation ( rays) are emitted by unstableatomic nuclei.

Proposed by Marie Curie to describe the emission of ionizing radiationby some of the heavier elements. Ionizing radiation interacts with matterto produce ions. Thus the radiation is sufficiently energetic to breakchemical bonds.

Some ionizing radiation is particulate (consisting of particles), and some isnonparticulate.

particulate: , , and particles

Nuclear EquationsA nuclear equation represents the changes that occur during a nuclear

process. The target nucleus and bombarding particle are represented on theleft side of the equation, and the product nucleus and ejected particle on theright side. A nuclear equation is written to conform to two rules:

1. The sum of mass numbers must be the same on both sides.

2. The sum of atomic numbers must be the same on both sides.

Alpha ParticlesAn alpha () particle is a combination of two protons and two neutrons

identical to the helium ion (4He2+). Alpha particles are emitted in someradioactive decay processes.

They produce large numbers of ions via their collisions and nearcollisions with atoms as they travel through matter, but their penetratingpower is low.

Because they have a positive charge, they are deflected by electric andmagnetic fields.

A reaction that produces an particle is also called an alpha decay.

23892U

23490Th +

42He

2

Beta ParticlesA beta particle ( particle) is an electron emitted as a result of the

conversion of a neutron to a proton in certain atomic nuclei undergoingradioactive decay.

particles are are electrons that originate from the nuclei of atoms innuclear decay processes

extremely energetic and do not end up in an orbital of the decaying atom

represented as either 0-1e or

their mass is exceedingly small relative to a nucleon

they have a negative (-) charge, and are thus deflected by electric andmagnetic fields

greater penetrating power through matter than particles

Beta EmissionIodine-131 is an isotope that undergoes decay by beta emission

13153I

13154Xe +

0-1e

Beta emission is equivalent to the conversion of a neutron to a proton.

10n

11H +

0-1e or n p +

Gamma RadiationGamma () rays are a form of electromagnetic radiation of high penetrating

power emitted by certain radioactive nuclei.

It changes neither the atomic number nor the mass number of a nucleus

represented as either 00 or simply .

Gamma radiation usually accompanies other radioactive emissionbecause it represents the energy lost when the nucleons in a nuclearreaction reorganize into more stable arrangements.

Often gamma rays are not explicitly shown when writing nuclearequations.

Summary of Properties

charge 2+ -1 0

mass (g) 6.64 1024 9.11 1028 0

relative penetrating 1 100 10,000power

nature of radiation 42He nuclei Electrons High-energyphotons

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Positron EmissionA positron (+, 0+1, or

0+1e) is a positive electron emitted as a result of the

conversion of a proton to a neutron in a radioactive nucleus.

same mass as electron, opposite in charge

positron emission causes the atomic number of the reactant to decreaseby 1

Examples of decays by positron emission

116C

115B +

0+1e

3015P

3014Si +

0+1e

Generally

11p

10n +

0+1e or p n +

+

Electron CaptureElectron capture is a mode of radioactive decay in which an inner-shell

orbital electron is captured by the nucleus.

When an electron from a higher quantum level drops to the energy levelvacated by the captured electron, X radiation is emitted.

Some examples are

8137Rb +

0-1e

8136Kr

20281Tl +

0-1e

20280Hg

Electron capture, like positron emission, has the effect of converting a protonto a neutron:

11p +

0-1e

10n

Particles in Nuclear ReactionsParticles found in nuclear reactions

particle symbol

neutron 10n or nproton 11H or pelectron 0-ealpha particle 42He or beta particle 0-1e or

positron 0+1e or +

Types of Radioactive Decay

change changetype nuclear equation in Z in A

alpha decay AZXA-4Z-2Y +

42He -2 -4

beta emission AZXA

Z+1Y +0-1e +1 unchanged

positron emission AZXA

Z-1Y +0

+1e -1 unchanged

electron capture AZX +0-1e

AZ-1Y -1 unchanged

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Radioactive Decay Modes

N

Z

Parent

atom

n

p

+ EC

en.wikipedia.org/wiki/File:Radioactive decay modes.svg

2 Patterns of Nuclear Stability

Neutron-to-Proton RatioNeutrons are involved in the strong nuclear force that keep positively

charged protons within a small volume.

As the number of protons in a nucleus increases, there is an ever greaterneed for neutrons to counteract the protonproton repulsions.

at Z 20, nneutrons nprotons

at Z > 20, nneutrons > nprotons

to create a stable nucleus increases more rapidly than the number ofprotons

Thus, the neutron-to-proton ratios of stable nuclei increase withincreasing atomic number

E.g., 126C (n/p = 1),5522Mn (n/p = 1.2),

19779Au (n/p 1.49)

Neutron-to-Proton Ratio

en.wikipedia.org/wiki/File:Table isotopes en.svg

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Belt of StabilityThe dark blue dots in the figure represent stable (nonradioactive) isotopes.

The region of the graph covered by these dark blue dots is known as the beltof stability.

The belt of stability ends at element 83 (bismuth).

All nuclei with 84 or more protons are radioactive.

Radioactive Decay PattersThe type of radioactive decay that a particular radionuclide undergoes

depends largely on how its neutron-to-proton ratio compares with those ofnearby nuclei that lie within the belt of stability. Three general situations:

1. Nuclei above the belt of stability (high neutron-to-proton ratios). Increasestability via emitting a beta particle.

2. Nuclei below the belt of stability (low neutron-to-proton ratios). Increasestability by increasing the number of neutrons via either positronemission or electron capture.

3. Nuclei with atomic numbers 84. These heavy nuclei tend to undergoalpha emission.

Predicting Modes of Nuclear DecayBLBMWS 13e, Exercise 21.3, p 916

Predict the mode of decay of

1. carbon-14,

2. xenon-118.

ANSWERS

1. emit a beta particle to decrease the n/p ratio:

146C

147N +

0-1e

2. either positron emission or electron capture

11854Xe

11853I +

0+1e

11854Xe +

0-1e

11853I

Radioactive Decay SeriesA radioactive decay series (or radioactive decay chain, or nuclear

disintegration series is a succession of individual steps whereby an initialradioactive isotope is ultimately converted to a stable isotope.

cannot gain stability by a single emission, occurs in a series of successiveemissions

Three such series occur in nature: uranium-238 to lead-206, uranium-235to lead-207, and thorium-232 to lead-208. All of the decay processes inthese series are either alpha emissions or beta emissions.

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Magic Numbers for Nuclear StabilityTwo further observations can help us to predict stable nuclei:

1. Nuclei with the magic numbers of 2, 8, 20, 28, 50, or 82 protons or 2, 8,20, 28, 50, 82, or 126 neutrons are generally more stable than nuclei thatdo not contain these numbers of nucleons.

2. Nuclei with even numbers of protons, neutrons, or both are more likelyto be stable than those with odd numbers of protons and/or neutrons.

60% of stable nuclei have an even number of both protons andneutrons, whereas less than 2% have odd numbers of both.

These can be understood in terms of the shell model of the nucleus.

nucleons reside in shells analogous to the shell structure for electronsin atoms, where certain numbers of electrons correspond to stablefilled-shell electron configurations.

Protons and Neutrons PairsEvidence also suggests that pairs of protons and pairs of neutrons have a

special stability, analogous to the pairs of electrons in molecules.

Thus stable nuclei with an even number of protons and/or neutrons arefar more numerous than those with odd numbers.

3 Nuclear Transmutations

Nuclear TransmutationsIn some nuclear reactions, the nucleus decays spontaneously. A nucleus

can also change identity if it is struck by a neutron or by another nucleus.Nuclear reactions induced in this way are known as nuclear transmutations.

In 1919, Ernest Rutherford performed the first conversion of one nucleusinto another, using alpha particles emitted by radium to convert nitrogen-14into oxygen-17

147N +

42He

178O +

11H or

147N +

178O + p

Shorthand NotationThe shorthand notation to represent nuclear transmutations

147N (,p)

178O

target nucleus 147Nbombarding particle ejected particle pproduct nucleus 178O

Writing a Balanced Nuclear EquationBLBMWS 13e, Example 21.4, p 918

Write the balanced nuclear equation for the process summarized as 2713Al(n,

) 2411Na.

ANSWER

2713Al +

10n

2411Na +

42He or

2713Al + n

2411Na +

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Accelerating Charged ParticlesA particle accelerator a device that uses strong magnetic and electrostatic

fields to accelerate charged particles.

Also called cyclotron, synchrotron, and atom smashers.

Alpha particles and other positively charged particles must move veryfast to overcome the electrostatic repulsion between them and the targetnucleus.

The charged particles can bemanipulated by electric andmagnetic fields.

They pass through tubes kept at high vacuum to avoid inadvertentcollisions with any gas-phase molecules.

Fermi National Accelerator Laboratory

en.wikipedia.org/wiki/File:Fermilab.jpg

Reactions Involving NeutronsNeutrons, because they are neutral, are not repelled by the nucleus and

do not need to be accelerated to cause nuclear reactions. The neutrons areproduced in nuclear reactors.

For example, synthesis of cobalt-60 from iron-58

5826Fe +

10n

5926Fe

5926Fe

5927Co +

0-1e

5927Co +

10n

6027Co

Transuranium ElementsTransuranium elements are elements that follow uranium in the periodic

table.

Elements 93 (neptunium, Np) and 94 (plutonium, Pu) were produced in1940 by bombarding uranium-238 with neutrons.

23892U +

10n

23992U

23993Np +

0-1e

23993Np +

10n

23994Pu +

0-1e

Elements with still larger atomic numbers are normally formed in smallquantities in particle accelerators. For example, by using alpha particles

23994Pu +

42He

24296Cm +

10n

Other elements can be used.

20882Pb +

7030Zn

277112Cn +

10n

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4 Rates of Radioactive Decay

Radioactive DecayRadioactive decay is a first-order kinetic process, which has a characteristic

half-life.

The half-life t1/2 of a reaction is the time required for one-half of a reactant tobe consumed. In a nuclear decay process, it is the time required for one-half ofthe atoms present in a sample to undergo radioactive decay.

Half-lives as short as millionths of a second and as long as billions ofyears are known.

unaffected by external conditions such as temperature, pressure, or stateof chemical combination, thus they cannot be rendered harmless bychemical reaction or by any other practical treatment

Half-Lives and Decay TypesThe half-lives and type of decay for several natural (N) or synthetic (S)

radioisotopes

N/S Isotope half-life (yr) type of decay

N 23892U 4.5 109 alpha

N 23592U 7.0 108 alpha

N 23290Th 1.4 1010 alpha

N 4019K 1.3 109 beta

N 146C 5700 beta

S 23994Pu 24,000 alphaS 13755Cs 30.2 betaS 9038Sr 28.8 betaS 13153I 0.022 beta

Calculation of Half-LivesBLBMWS 13e, Exercise 21.5, p 921

The half-life of cobalt-60 is 5.27 yr. How much of a 1.000-mg sample ofcobalt-60 is left after 15.81 yr?

ANSWER: 0.125 mg

Radioactive Decay LawThe radioactive decay law states that the rate of decay of a radioactive

materialthe activity, Ais directly proportional to the number of atomspresent.

The rate for a first-order kinetic process is

Rate = kN

where N is the number of radioactive nuclei and k is the decay constant.

Activity and Decay RateThe rate at which a sample decays is called its activity.

The becquerel (Bq) is the SI unit for expressing activity. A becquerel isdefined as one nuclear disintegration per second.

An older, but still widely used, unit of activity is the curie (Ci), definedas 3.7 1010 disintegrations per second, which is the rate of decay of 1 gof radium.

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First-Order Rate LawA first-order rate law (Rate = kN) can be transformed into

lnNtN0

= kt

where t is the time interval of decay, k is the decay constant, N0 is the initialnumber of nuclei (at time zero), and Nt is the number remaining after the timeinterval.

The relationship between the decay constant k and half-life t1/2 is

k =0.693

t1/2

using the value ln(Nt/N0) = ln(0.5) = 0.693 for one half-life.

Calculating the Age of ObjectsBLBMWS 13e, Exercise 21.6, p 924

A rock contains 0.257 mg of lead-206 for every milligram of uranium-238.The half-life for the decay of uranium-238 to lead-206 is 4.5 109 yr. How oldis the rock?

ANSWER: 1.7 109 yr

Radioactive Decay and TimeBLBMWS 13e, Exercise 21.7, pp 924-925

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

1. What is the half-life of strontium-90?

2. How much strontium-90 will remain after 5.00 yr?

3. What is the initial activity of the sample in becquerels and curies?

ANSWERS:

1. t1/2 = 28.8 yr

2. Nt = 0.887 g

3. 5.1 102 disintegrations/s or 1.4 102 Ci

5 Detection of Radioactivity

Geiger CounterRadioactivity can be detected and measured by aGeiger counter.

Radiation is able to ionize matter. The ions and electrons produced bythe ionizing radiation permit conduction of an electrical current.

A current pulse between the anode and the metal cylinder occurswhenever entering radiation produces ions. Each pulse is counted inorder to estimate the amount of radiation.

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Geiger Counter

VoltageSource

Counter Resistor

Cathode

GammaRadiation

R

InputWindow

commons.wikimedia.org/wiki/File:Geiger Mueller Counter with Circuit-en.svg

6 Energetics of Nuclear Reactions

Energy of Nuclear ReactionsIn order to understand the great amount of energy released in nuclear

reactions as compared to chemical reactions, we start with Einsteins equationfrom the theory of relativity that relates mass and energy: E = mc2

The mass changes in chemical reactions are too small to detect, thus massis conserved. E.g., the mass change in the combustion of 1 mol of CH4 is9.9 109 g.

Themass changes and the associated energy changes in nuclear reactionsare much greater than those for chemical reactions.

Mass and Energy Change in Uranium-238 DecayGiven the alpha decay of uranium-238

23892U

23490Th +

42He

The mass change is the total mass of the products minus the total mass of thereactants.

233.9942 g+ 4.0015 g 238.0003 g = 0.0046 g

The energy change per mole associated with this reaction is

E = (mc2) = c2m

= (2.9979 108 m/s)2 0.0046 g = 4.1 1011 J

Mass DefectScientists discovered in the 1930s that the masses of nuclei are always less

than the masses of the individual nucleons of which they are composed.

mass of 42He is 4.00150 amu, mass of 1 p is 1.00728 amu, mass of 1 n is1.00866 amu

mass 2 p + 2 n >mass 42He, with a mass difference of 0.03038 amu

The mass difference between a nucleus and its constituent nucleons is calledthemass defect.

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Nuclear Binding EnergyEnergy must be added to a nucleus to break it into separated protons and

neutrons

Energy + 42He 211H + 2

10n

The mass change for the conversion of helium-4 into separated nucleons ism = 0.03038 amu. Using E = mc2, thus

E = c2m = 4.534 1012 J

The energy required to separate a nucleus into its individual nucleons is calledthe nuclear binding energy.

Some Binding EnergiesMass (m) defects and binding energies (BE) for three nuclei (masses in amu,

energy in J).

42He

5626Fe

23892U

m of nucleus 4.00150 55.92068 238.00031mtot of nucleons 4.03188 56.44914 239.93451mass defect m 0.03038 0.52846 1.93420BE 4.53 1012 7.90 1011 2.89 1010

BE per nucleon 1.13 1012 1.41 1012 1.21 1012

Nuclear Stability and Binding EnergyValues of BE per nucleon can be used to compare the stabilities of different

combinations of nucleons.

BE per nucleon at first increases until 1.4 1012 J for nuclei with A A(iron-56).

BE then decreases to about 1.2 1012 J for very heavy nuclei

Nuclei of intermediate mass numbers are more tightly bound, thus morestable, than those with either smaller or larger mass numbers.

Fission and FusionThis trend has two significant consequences

1. Heavy nuclei gain stability and therefore give off energy if they arefragmented into two mid-sized nuclei. This process is known as fission.Used to generate energy in nuclear power plants.

2. Due to the sharp increase in the graph for small mass numbers, evengreater amounts of energy are released if very light nuclei are combined,or fused together, to give more massive nuclei. This fusion process is theessential energy-producing process in the sun and other stars.

7 Nuclear Power: Fission

Fission of Uranium-235Two ways that the uranium-235 nucleus splits are

10n +

23592U

13752Te +

9740Zr + 2

10n

14256Ba +9136Kr + 3

10n

The nuclei produced are called the fission products.

also radioactive and undergo further nuclear decay

fission products of 23592U more than 200 isotopes of 35 elements, most ofthem radioactive

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Chain ReactionsInitial absorption of the neutron by the nucleus. The resulting more

massive nucleus is often unstable and spontaneously undergoes fission.

Slow-moving neutrons are required, fast neutrons tend to bounce off thenucleus.

Each reaction produces more neutrons, causing further fission, causing a chainreaction.

The number of fissions and the energy released quickly escalate, and ifthe process is unchecked, the result is a violent explosion.

Critical and Supercritical MassThe minimum amount of fissionable material large enough to maintain a

chain reaction with a constant rate of fission is called the critical mass.

The critical mass of uranium-235 is about 50 kg for a bare sphere of themetal.

If more than a critical mass of fissionable material is present, very few neutronsescape. The chain reaction thus multiplies the number of fissions, which canlead to a nuclear explosion. A mass in excess of a critical mass is referred to asa supercritical mass.

Nuclear ReactorsNuclear power plants use nuclear fission to generate energy. Four principal

components of the core

1. Fuel elements. A fissionable substance, e.g., uranium-235.

2. Control rods. Materials that absorb neutrons, such as boron-10 or analloy of silver, indium, and cadmium. These rods regulate the flux ofneutrons to keep the reaction chain self-sustaining and also prevent thereactor core from overheating.

3. Moderator. These slow down the neutrons ( few km/s) so that theycan be captured more readily by the fissionable nuclei. E.g., water orgraphite.

4. Primary coolant. Transports the heat generated by the nuclear chainreaction away from the reactor core. E.g. water.

8 Nuclear Power: Fusion

Fusion in the SunSpectroscopic studies indicate that the mass composition of the Sun is 73%

H, 26% He, and only 1% all other elements. The following reactions are amongthe numerous fusion processes believed to occur in the Sun:

11H +

11H

21H +

0+1e

11H +

21H

32He

32He +

32He

42He + 2

11H

32He +

11H

42He +

0+1e

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Fusion as an Energy SourceFusion is appealing as an energy source because of the availability of light

isotopes on Earth and because fusion products are generally not radioactive.Despite this fact, fusion is not presently used to generate energy.

Extremely high temperatures and pressures are needed to overcome theelectrostatic repulsion between nuclei in order to fuse them. Fusionreactions are therefore also known as thermonuclear reactions. Thelowest temperature required for any fusion is about 40,000,000 K, thetemperature needed to fuse deuterium and tritium.

No known structural material is able to with stand the enormoustemperatures necessary for fusion.

Even with the current technology, scientists have not yet been able to generatemore power than is consumed over a sustained period of time.

9 Effect of Nuclear Radiation on Matter

Ionizing RadiationRadiation energy can cause atoms in the matter to be either excited or

ionized.

Ionizing radiation is radiation that causes ionization. It is far moreharmful to biological systems than nonionizing radiation

Nonionizing radiation is low in energy and does not cause ionization.Slow-moving. E.g., radiofrequency electromagnetic radiation.

Ionization of WaterMost living tissue contains at least 70% water by mass. Water absorbs most

of the energy of the radiation. Thus, it is common to define ionizing radiationas radiation that can ionize water, > 1216 kJ/mol.

, , rays, X-rays and higher-energy ultraviolet radiation are forms ofionizing radiation.

When ionizing radiation passes through living tissue, electrons are removedfrom H2O, forming highly reactive H2O

+ ions, which then produces theunstable and highly reactive free radical OH (hydroxyl radical).

H2O+ + H2O H3O

+ + OH

In cells and tissues, OH can attack biomolecules to produce new free radicals,which in turn attack yet other biomolecules. Thus a few OH radicals caninitiate a large number of chemical reactions that are ultimately able to disruptthe normal operations of cells.

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