13_ChangesInTheNucleus_2a

CHEM 16 GENERAL CHEMISTRY 1

13 CHANGES IN THE NUCLEUS

Dr. Gil C. Claudio

University of the Philippines, Diliman

First Semester 2014-2015

TABLE OF CONTENTS

RADIOACTIVITY AND NUCLEAR EQUATIONS

PATTERNS OF NUCLEAR STABILITY

NUCLEAR TRANSMUTATIONS

RATES OF RADIOACTIVE DECAY

DETECTION OF RADIOACTIVITY

ENERGETICS OF NUCLEAR REACTIONS

NUCLEAR POWER: FISSION

NUCLEAR POWER: FUSION

EFFECT OF NUCLEAR RADIATION ON MATTER

REFERENCES

References of these notes

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

Chemistry: The Central Science, 13th ed., by TheodoreL. Brown, H. Eugene LeMay Jr., Bruce E. Bursten, CatherineJ. Murphy, Patrick M. Woodward, and Matthew W. Stoltzfus.

NUCLEAR CHEMISTRY

Nuclear chemistry is the study of nuclear reactions, with anemphasis on their uses and their effects on biological systems.

energy and medical applications

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

ISOTOPES AND NUCLIDES

Atoms with the same atomic number but different mass numbersare known as isotopes.

The mass number is the total number of nucleons in thenucleus.

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

E.g., the three naturally occurring isotopes of uranium areuranium-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 protonsand neutrons.

Nuclides that are radioactive are called radionuclides, andatoms containing these nuclei are called radioisotopes.

RADIOACTIVITY

Radioactivity is a phenomenon in which small particles of matter( or particles) and/or electromagnetic radiation ( rays) areemitted by unstable atomic nuclei.

Proposed by Marie Curie to describe the emission of ionizingradiation by some of the heavier elements. Ionizing radiationinteracts with matter to produce ions. Thus the radiation issufficiently energetic to break chemical bonds.

Some ionizing radiation is particulate (consisting of particles), andsome is nonparticulate.

particulate: , , and particles

NUCLEAR EQUATIONS

A nuclear equation represents the changes that occur during anuclear process. The target nucleus and bombarding particle arerepresented on the left side of the equation, and the productnucleus and ejected particle on the right side. A nuclear equationis 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 PARTICLES

An alpha () particle is a combination of two protons and twoneutrons identical to the helium ion (4He2+). Alpha particles areemitted in some radioactive decay processes.

They produce large numbers of ions via their collisions andnear collisions with atoms as they travel through matter, buttheir penetrating power is low.

Because they have a positive charge, they are deflected byelectric and magnetic fields.

A reaction that produces an particle is also called an alphadecay.

23892U

23490Th +

42He

BETA PARTICLES

A beta particle ( particle) is an electron emitted as a result ofthe conversion of a neutron to a proton in certain atomic nucleiundergoing radioactive decay.

particles are are electrons that originate from the nuclei ofatoms in nuclear decay processes

extremely energetic and do not end up in an orbital of thedecaying 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 byelectric and magnetic fields

greater penetrating power through matter than particles

BETA EMISSION

Iodine-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 aproton.

10n

11H +

0-1e or n p +

GAMMA RADIATION

Gamma () rays are a form of electromagnetic radiation of highpenetrating power emitted by certain radioactive nuclei.

It changes neither the atomic number nor the mass number ofa nucleus

represented as either 00 or simply .

Gamma radiation usually accompanies other radioactiveemission because it represents the energy lost when thenucleons in a nuclear reaction reorganize into more stablearrangements.

Often gamma rays are not explicitly shown when writingnuclear equations.

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

POSITRON EMISSION

A positron (+, 0+1, or0

+1e) is a positive electron emitted as aresult of the conversion of a proton to a neutron in a radioactivenucleus.

same mass as electron, opposite in charge

positron emission causes the atomic number of the reactantto decrease by 1

Examples of decays by positron emission

116C

115B +

0+1e

3015P

3014Si +

0+1e

Generally

11p

10n +

0+1e or p n +

+

ELECTRON CAPTURE

Electron capture is a mode of radioactive decay in which aninner-shell orbital electron is captured by the nucleus.

When an electron from a higher quantum level drops to theenergy level vacated by the captured electron, X radiation isemitted.

Some examples are

8137Rb +

0-1e

8136Kr

20281Tl +

0-1e

20280Hg

Electron capture, like positron emission, has the effect ofconverting a proton to a neutron:

11p +

0-1e

10n

PARTICLES IN NUCLEAR REACTIONS

Particles found in nuclear reactions

particle symbol

neutron 10n or n

proton 11H or pelectron 0-e

alpha 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 AZX A-4

Z -2Y +42He -2 -4

beta emission AZX A

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

positron emission AZX A

Z -1Y +0

+1e -1 unchanged

electron capture AZX + 0-1e

A

Z -1Y -1 unchanged

RADIOACTIVE DECAY MODES

N

Z

Parent

atom

n

p

+ EC

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

NEUTRON-TO-PROTON RATIO

Neutrons are involved in the strong nuclear force that keeppositively charged protons within a small volume.

As the number of protons in a nucleus increases, there is anever greater need for neutrons to counteract the protonprotonrepulsions.

at Z 20, nneutrons nprotons

at Z > 20, nneutrons > nprotons

to create a stable nucleus increases more rapidly than thenumber of protons

Thus, the neutron-to-proton ratios of stable nuclei increasewith increasing 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

BELT OF STABILITY

The dark blue dots in the figure represent stable (nonradioactive)isotopes. The region of the graph covered by these dark blue dotsis known as the belt of stability.

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

All nuclei with 84 or more protons are radioactive.

RADIOACTIVE DECAY PATTERS

The type of radioactive decay that a particular radionuclideundergoes depends largely on how its neutron-to-proton ratiocompares with those of nearby nuclei that lie within the belt ofstability. Three general situations:

1. Nuclei above the belt of stability (high neutron-to-protonratios). Increase stability via emitting a beta particle.

2. Nuclei below the belt of stability (low neutron-to-protonratios). Increase stability by increasing the number ofneutrons via either positron emission or electron capture.

3. Nuclei with atomic numbers 84. These heavy nuclei tendto undergo alpha 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 capture11854Xe

11853I +

0+1e

11854Xe +

0-1e

11853I

RADIOACTIVE DECAY SERIES

A radioactive decay series (or radioactive decay chain, ornuclear disintegration series is a succession of individual stepswhereby an initial radioactive isotope is ultimately converted to astable isotope.

cannot gain stability by a single emission, occurs in a series ofsuccessive emissions

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

MAGIC NUMBERS FOR NUCLEAR STABILITY

Two further observations can help us to predict stable nuclei:

1. Nuclei with the magic numbers of 2, 8, 20, 28, 50, or 82protons or 2, 8, 20, 28, 50, 82, or 126 neutrons are generallymore stable than nuclei that do not contain these numbers ofnucleons.

2. Nuclei with even numbers of protons, neutrons, or both aremore likely to be stable than those with odd numbers ofprotons and/or neutrons.

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

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

nucleons reside in shells analogous to the shell structure forelectrons in atoms, where certain numbers of electronscorrespond to stable filled-shell electron configurations.

PROTONS AND NEUTRONS PAIRS

Evidence also suggests that pairs of protons and pairs of neutronshave a special stability, analogous to the pairs of electrons inmolecules.

Thus stable nuclei with an even number of protons and/orneutrons are far more numerous than those with odd numbers.

NUCLEAR TRANSMUTATIONS

In some nuclear reactions, the nucleus decays spontaneously. Anucleus can also change identity if it is struck by a neutron or byanother nucleus. Nuclear reactions induced in this way are knownas nuclear transmutations.

In 1919, Ernest Rutherford performed the first conversion of onenucleus into another, using alpha particles emitted by radium toconvert nitrogen-14 into oxygen-17

147N +

42He

178O +

11H or

147N +

178O + p

SHORTHAND NOTATION

The shorthand notation to represent nuclear transmutations

147N (,p)

178O

target nucleus 147Nbombarding particle ejected particle p

product nucleus 178O

WRITING A BALANCED NUCLEAR EQUATIONBLBMWS 13E, EXAMPLE 21.4, P 918

Write the balanced nuclear equation for the process summarized as2713Al(n, )

2411Na.

ANSWER

2713Al +

10n

2411Na +

42He or

2713Al + n

2411Na +

ACCELERATING CHARGED PARTICLES

A particle accelerator a device that uses strong magnetic andelectrostatic fields to accelerate charged particles.

Also called cyclotron, synchrotron, and atom smashers.

Alpha particles and other positively charged particles mustmove very fast to overcome the electrostatic repulsionbetween them and the target nucleus.

The charged particles can be manipulated by electric andmagnetic fields.

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

FERMI NATIONAL ACCELERATOR LABORATORY

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

REACTIONS INVOLVING NEUTRONS

Neutrons, because they are neutral, are not repelled by the nucleusand do not need to be accelerated to cause nuclear reactions. Theneutrons are produced in nuclear reactors.

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

5826Fe +

10n

5926Fe

5926Fe

5927Co +

0-1e

5927Co +

10n

6027Co

TRANSURANIUM ELEMENTS

Transuranium elements are elements that follow uranium in theperiodic table.

Elements 93 (neptunium, Np) and 94 (plutonium, Pu) wereproduced in 1940 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 formedin small quantities in particle accelerators. For example, byusing alpha particles

23994Pu +

42He

24296Cm +

10n

Other elements can be used.20882Pb +

7030Zn

277112Cn +

10n

RADIOACTIVE DECAY

Radioactive decay is a first-order kinetic process, which has acharacteristic half-life.

The half-life t1/2 of a reaction is the time required for one-half of areactant to be consumed. In a nuclear decay process, it is the timerequired for one-half of the atoms present in a sample to undergoradioactive decay.

Half-lives as short as millionths of a second and as long asbillions of years are known.

unaffected by external conditions such as temperature,pressure, or state of chemical combination, thus they cannotbe rendered harmless by chemical reaction or by any otherpractical treatment

HALF-LIVES AND DECAY TYPES

The 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 alpha

S 13755Cs 30.2 beta

S 9038Sr 28.8 beta

S 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-mgsample of cobalt-60 is left after 15.81 yr?

ANSWER: 0.125 mg

RADIOACTIVE DECAY LAW

The radioactive decay law states that the rate of decay of aradioactive materialthe activity, Ais directly proportional to thenumber of atoms present.

The rate for a first-order kinetic process is

Rate = kN

where N is the number of radioactive nuclei and k is the decayconstant.

ACTIVITY AND DECAY RATE

The rate at which a sample decays is called its activity.

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

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

FIRST-ORDER RATE LAW

A first-order rate law (Rate = kN) can be transformed into

lnNt

N0= kt

where t is the time interval of decay, k is the decay constant, N0 isthe initial number of nuclei (at time zero), and Nt is the numberremaining after the time interval.

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 ofuranium-238. The half-life for the decay of uranium-238 tolead-206 is 4.5 109 yr. How old is 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 after2.00 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 andcuries?

ANSWERS:

1. t1/2 = 28.8 yr

2. Nt = 0.887 g

3. 5.1 102 disintegrations/s or 1.4 102 Ci

GEIGER COUNTER

Radioactivity can be detected and measured by a Geiger counter.

Radiation is able to ionize matter. The ions and electronsproduced by the ionizing radiation permit conduction of anelectrical current.

A current pulse between the anode and the metal cylinderoccurs whenever entering radiation produces ions. Each pulseis counted in order to estimate the amount of radiation.

GEIGER COUNTER

VoltageSource

Counter Resistor

Cathode

GammaRadiation

R

InputWindow

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

ENERGY OF NUCLEAR REACTIONS

In order to understand the great amount of energy released innuclear reactions as compared to chemical reactions, we start withEinsteins equation from the theory of relativity that relates massand energy: E = mc2

The mass changes in chemical reactions are too small todetect, thus mass is conserved. E.g., the mass change in thecombustion of 1 mol of CH4 is 9.9 10

9 g.

The mass changes and the associated energy changes innuclear reactions are much greater than those for chemicalreactions.

MASS AND ENERGY CHANGE IN URANIUM-238

DECAY

Given the alpha decay of uranium-238

23892U

23490Th +

42He

The mass change is the total mass of the products minus the totalmass of the reactants.

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 DEFECT

Scientists discovered in the 1930s that the masses of nuclei arealways less than the masses of the individual nucleons of whichthey are composed.

mass of 42He is 4.00150 amu, mass of 1 p is 1.00728 amu,mass of 1 n is 1.00866 amu

mass 2 p + 2 n > mass 42He, with a mass difference of0.03038 amu

The mass difference between a nucleus and its constituentnucleons is called the mass defect.

NUCLEAR BINDING ENERGY

Energy must be added to a nucleus to break it into separatedprotons and neutrons

Energy + 42He 211H + 2

10n

The mass change for the conversion of helium-4 into separatednucleons is m = 0.03038 amu. Using E = mc2, thus

E = c2m = 4.534 1012 J

The energy required to separate a nucleus into its individualnucleons is called the nuclear binding energy.

SOME BINDING ENERGIES

Mass (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 ENERGY

Values of BE per nucleon can be used to compare the stabilities ofdifferent combinations of nucleons.

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

BE then decreases to about 1.2 1012 J for very heavynuclei

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

FISSION AND FUSION

This trend has two significant consequences

1. Heavy nuclei gain stability and therefore give off energy if theyare fragmented into two mid-sized nuclei. This process isknown as fission. Used to generate energy in nuclear powerplants.

2. Due to the sharp increase in the graph for small massnumbers, even greater amounts of energy are released if verylight nuclei are combined, or fused together, to give moremassive nuclei. This fusion process is the essentialenergy-producing process in the sun and other stars.

FISSION OF URANIUM-235

Two 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 35elements, most of them radioactive

CHAIN REACTIONS

Initial absorption of the neutron by the nucleus. The resultingmore massive nucleus is often unstable and spontaneouslyundergoes fission.

Slow-moving neutrons are required, fast neutrons tend tobounce off the nucleus.

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

The number of fissions and the energy released quicklyescalate, and if the process is unchecked, the result is aviolent explosion.

CRITICAL AND SUPERCRITICAL MASS

The minimum amount of fissionable material large enough tomaintain a chain reaction with a constant rate of fission is calledthe critical mass.

The critical mass of uranium-235 is about 50 kg for a baresphere of the metal.

If more than a critical mass of fissionable material is present, veryfew neutrons escape. The chain reaction thus multiplies thenumber of fissions, which can lead to a nuclear explosion. A massin excess of a critical mass is referred to as a supercritical mass.

NUCLEAR REACTORS

Nuclear power plants use nuclear fission to generate energy. Fourprincipal components of the core

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

2. Control rods. Materials that absorb neutrons, such asboron-10 or an alloy of silver, indium, and cadmium. Theserods regulate the flux of neutrons to keep the reaction chainself-sustaining and also prevent the reactor core fromoverheating.

3. Moderator. These slow down the neutrons ( few km/s) sothat they can be captured more readily by the fissionablenuclei. E.g., water or graphite.

4. Primary coolant. Transports the heat generated by thenuclear chain reaction away from the reactor core. E.g. water.

FUSION IN THE SUN

Spectroscopic studies indicate that the mass composition of theSun is 73% H, 26% He, and only 1% all other elements. Thefollowing reactions are among the numerous fusion processesbelieved to occur in the Sun:

11H +

11H

21H +

0+1e

11H +

21H

32He

32He +

32He

42He + 2

11H

32He +

11H

42He +

0+1e

FUSION AS AN ENERGY SOURCE

Fusion is appealing as an energy source because of the availabilityof light isotopes on Earth and because fusion products aregenerally not radioactive. Despite this fact, fusion is not presentlyused to generate energy.

Extremely high temperatures and pressures are needed toovercome the electrostatic repulsion between nuclei in order tofuse them. Fusion reactions are therefore also known asthermonuclear reactions. The lowest temperature requiredfor any fusion is about 40,000,000 K, the temperature neededto fuse deuterium and tritium.

No known structural material is able to with stand theenormous temperatures necessary for fusion.

Even with the current technology, scientists have not yet been ableto generate more power than is consumed over a sustained periodof time.

IONIZING RADIATION

Radiation energy can cause atoms in the matter to be eitherexcited or ionized.

Ionizing radiation is radiation that causes ionization. It is farmore harmful to biological systems than nonionizing radiation

Nonionizing radiation is low in energy and does not causeionization. Slow-moving. E.g., radiofrequency electromagneticradiation.

IONIZATION OF WATER

Most living tissue contains at least 70% water by mass. Waterabsorbs most of the energy of the radiation. Thus, it is common todefine ionizing radiation as radiation that can ionize water, > 1216kJ/mol.

, , rays, X-rays and higher-energy ultraviolet radiation areforms of ionizing radiation.

When ionizing radiation passes through living tissue, electrons areremoved from H2O, forming highly reactive H2O

+ ions, which thenproduces the unstable and highly reactive free radical OH (hydroxylradical).

H2O+ + H2O H3O

+ + OH

In cells and tissues, OH can attack biomolecules to produce newfree radicals, which in turn attack yet other biomolecules. Thus afew OH radicals can initiate a large number of chemical reactionsthat are ultimately able to disrupt the normal operations of cells.

Radioactivity and Nuclear EquationsPatterns of Nuclear StabilityNuclear TransmutationsRates of Radioactive DecayDetection of RadioactivityEnergetics of Nuclear ReactionsNuclear Power: FissionNuclear Power: FusionEffect of Nuclear Radiation on Matter