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Atomic & Nuclear Structure

Dr. F. Z. KhiariDepartment of Physics

King Fahd University of Petroleum & Minerals

Dhahran, Saudi Arabia

Periodic Table of The Elements

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Nuclear Notation: Nuclides

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Isotopes

Nuclear Units: Dimension

• Nuclear sizes are quite small and need smaller units:smaller units:

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Nuclear Units:Mass

• Nuclear masses are measured in terms ofatomic mass units (amu, u) with the carbon-12 nucleus defined as having a mass of12 nucleus defined as having a mass ofexactly 12 amu. It is also common practice toquote the rest mass energy E = mc2 as if itwere the mass. The conversion to amu is:

Nuclear Units: Energy• Nuclear energies are very high compared to

atomic processes, and need larger units

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Constituents of Atoms

Constituents of Atoms

While the charges and masses are preciselyknown, the size is not. Our best information aboutthe proton and neutron indicates that they arethe proton and neutron indicates that they areconstituent particles. However we can attribute tothem a radius of about

1.2 x 10-15 meters = 1.2 fm

The electron is a fundamental particle which ispapparently not made out of any constituentparticles.

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Z Isotope Mass Number

Atomic Mass of Isotope

Abundance [%]

Atomic Mass of Element

1 H D T

1 2 3

1.0078250321 2.0141017780 3.0160492675

99.9885 0.0115

1.00794

Atomic Mass

2 He 3 4

3.016029309 74.0026032497

0.00013799.999863

4.002602

3 Li 6 7

6.015122 3 7.016004 0

7.59 92.41

6.941

4 Be 9 9.012182 100 9.012182 5 B 10

11 10.012937 11.0093055

19.9 80.1

10.811

6 C 12 13

12.0000000 13 0033548378

98.93 1 07

12.0107 13 14

13.003354837814.003241988

1.07

7 N 14 15

14.003 0740052 15.0001088984

99.632 0.368

14.0067

8 O 16 17 18

15.9949146221 16.99913150 17.9991604

99.757 0.038 0.205

15.9994

The Mole• A mole (abbreviated mol) of a pure substance is

a mass of the material in grams which isnumerically equal to the molecular mass. Anumerically equal to the molecular mass. Amole of any material will contain Avogadro'snumber of molecules. For example, carbon-12has an atomic mass of exactly 12.0 atomic massunits -- a mole of carbon-12 is therefore 12grams.

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Nuclear Forces

Nuclear Binding Energy• Nuclei are made up of protons and neutron, but the mass

of a nucleus is always less than the sum of the individualmasses of the protons and neutrons which constitute itmasses of the protons and neutrons which constitute it.The difference is a measure of the nuclear binding energywhich holds the nucleus together. This binding energy canbe calculated from the Energy - Mass relationship:

Nuclear Binding Energy: BE = mc2

m = Z.mp + N.mn – M(A,Z)

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Nuclear Binding Energy• For the alpha particle m = 0.03035 u which

gives a binding energy of 28.3 MeV

Nuclear Binding Energy Curve

• The binding energy curve is obtained bydividing the total nuclear binding energy by thenumber of nucleons: BE/A

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Fission

X + n fission Y* + Z* + neutrons

M(Y) + M(Z) + m(neutrons) < M(X) + m(n)

M = M(X) + m(n) - M(Y) - M(Z) - m(neutrons)

E = M c2E = M.c

Fission Fragments

• When 235U undergoes fission,the average of the fragmentthe average of the fragmentmass is about 118, but veryfew fragments near thataverage are found. It is muchmore probable to break upinto unequal fragments, andthe most probable fragmentmasses are around mass 95and 137.

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Uranium Fission

Fusion

X + Y fusion Z + nucleon

M(Z) + m(nucleon) < M(X) + M(Y)

M = M(X) + M(Y) – M(Z) – m(nucleon)

E = M.c2

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Proton-Proton Fusion• This is the nuclear fusion process which fuels the Sun

and other stars which have core temperatures lessthan 15 million Kelvin. A reaction cycle yields about25 MeV of energy25 MeV of energy

Deuterium-Tritium Fusion• For potential nuclear energy sources for the Earth,

the deuterium-tritium fusion reaction contained bysome kind of magnetic confinement seems the mostglikely path.

• The reaction yields 17.6 MeV of energy butrequires a temperature of approximately 40million Kelvins to overcome the coulomb barrierand ignite it. The deuterium fuel is abundant, buttritium must be either bred from lithium or gottentritium must be either bred from lithium or gottenin the operation of the deuterium cycle.

2H + 3H 4He + n + 17.6 MeV

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Summary

• Elements & Atoms

• Nucleus & electrons

• Protons and Atomic Number Z

• Isotopes and Neutron Number N

• Nucleons and Mass Number A

• Conservation of Z and A in all nuclear processes

• Atomic Mass Unit u

• Mole and Avogadro’s Number NA

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Radioactivity

Dr. F. Z. KhiariPhysics Department

King Fahd University of Petroleum and Minerals

Dhahran, Saudi Arabia

Radioactivity

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Nuclear Notation

• Standard nuclear notation shows the chemical symbol, the mass number and the atomic number of the isotope:atomic number of the isotope:

Isotopes

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Chart of the Nuclides

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NRadioactivity

• Radioactivity refers to the particles which areemitted from nuclei as a result of nuclearinstabilityinstability.

• Because the nucleus experiences the intenseconflict between the two strongest forces innature, it should not be surprising that there aremany nuclear isotopes which are unstable andemit some kind of radiation.

h f di i ll d• The most common types of radiation are called, , and radiation, but there are several othervarieties of radioactive decay.

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Radioactivity

• Radioactive decays are normally stated in termsof their half-lives, and the half-life of a givennuclear species is related to its radiation risk.

• The radioactive half-life for a given radioisotopeis a measure of the tendency of the nucleus to"decay" or "disintegrate" and as such is based

l b bilitpurely upon probability.

Radioactive Half-Life• The radioactive half-life for a given radioisotope is the

time for half the radioactive nuclei in any sample toundergo radioactive decay. After two half-lives, therewill be one fourth the original sample after three half-will be one fourth the original sample, after three half-lives one eight the original sample, and so forth.

A = Ao(1/2)t/T1/2

A = Ao(1/2)n

t = nT1/2

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Radioactive Half-Life

• The half-life is independent of the physicalstate (solid, liquid, gas), temperature,( , q , g ), p ,pressure, the chemical compound in whichthe nucleus finds itself, and essentially anyother outside influence.

• It is independent of the chemistry of theatomic surface, and independent of theordinary physical factors of the outsideordinary physical factors of the outsideworld.

Nuclear Decay Probability• Radioactive decay is a statistical process which

depends upon the instability of the particularradioisotope, but which for any given nucleus in asample is completely unpredictable. The decay processcan be described by assuming that individual nucleardecays are purely random events.

• If there are N radioactive nuclei at some time t, thenthe number -N which would decay in any given timeinterval t would be proportional to N:

Where is a constant of proportionality (decay constant).

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Nuclear Decay ProbabilityWithout any further assumptions, this leads to the exponential radioactive decay law:

This implies that the decay rate and amount of emittedradiation also follow the same type of relationship. Thenumber of atoms, the mass of the substance, and thelevel of activity all follow the same exponential decayform:

Radioactive Decay ConstantThe decay constant is also sometimes called thedisintegration constant.The half-life and the decay constant give the samey ginformation, so either may be used to characterizedecay.Another useful concept in radioactive decay is theMean lifetime. The Mean lifetime is the reciprocalof the decay constant .

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RadioactivityThe predictions of decaycan be stated in terms of thehalf-life , the decayhalf life , the decayconstant, or the mean(average) lifetime. Therelationship between thesequantities is as follows:

Activity

• The activity of a radioactive substance is definedas the number of radioactive nuclei thatdisintegrate per second.g p

A = |N/ t|

A = N= No e t

Ao = No

A(t) = Ao e t

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Units of Activity

• The SI unit of activity is the Becquerel [Bq]

1 Bq = 1 disintegration/sec (dps)

• The Curie [Ci] = Activity of 1g of 226Ra

1 Ci = 3.7 1010 Bq

Units of Activity

•1 kBq = 103 Bq

•1 MBq = 106 Bq

•1 mCi = 103 Ci

1 Ci 10 6 Ci

•1 MBq = 10 Bq

•1 GBq = 109 Bq

•1 TBq = 1012 Bq

•1 Ci = 106 Ci

•1 nCi = 109 Ci

•1 pCi = 1012 Ci

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Specific Activity (SA)

• (SA)mass = Activity/Mass [Bq/g]

• (SA)surface = Activity/Area [Bq/cm2]

• (SA)volume = Activity/Volume [Bq/cm3]

Radioactive Equilibrium

N1 N21

21 2

Secular Equilibrium: T1/2 >> T1/2 2 >> 1

1N1 = 2N2

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Radioactive Equilibrium

N1 N21

2

Transient Equilibrium: T1/2 > T1/2 2 > 1

A2/A1 = 2/(2- 1)

Summary

- Half-life

- Decay Constant

- Mean Lifetime

- Activity

- Units of Activity

- Specific Activity

- Radioactive Equilibrium

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12/31/2011

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Radioactive Decay Processes

F. Z. KhiariPhysics Department

King Fahd University of Petroleum and Minerals

Dhahran, Saudi Arabia

Alpha, Beta, and Gamma• Historically, the products of radioactivity were

called alpha, beta, and gamma when it was foundthat they could be analyzed into three distinctspecies by either a magnetic field or an electricfield:

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Penetration of Matter

• Though the most massive and mostenergetic of radioactive emissions, the alphag , pparticle is the shortest in range because ofits strong interaction with matter. Theelectromagnetic gamma ray is extremelypenetrating, even penetrating considerablethicknesses of concrete. The electron of betaradioactivity strongly interacts with matterand has a short range.

Penetration of Matter

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Alpha Decay

AZX

A4Z2Y 4

2 HeZ

Q = (MX MY M)c2 0

KE [(A-4)/A]Q 4 – 9 MeV

Discrete Energy Spectrum

Discrete Alpha Energies

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Alpha Barrier Penetration

Beta Radioactivity

• Beta particles are justelectrons from thenucleus, the term "betaparticle" being anhistorical term used inthe early description ofradioactivity. The highenergy electrons havegygreater range ofpenetration than alphaparticles, but still muchless than gamma rays.

The emission of the electron'santiparticle, the positron, is

also called beta decay.

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Beta Decay

AZX

AZ1Y 0

1e 00

Q = (MX MY Me)c2 0

AZX

AZ1Y 0

+1e 00

Continuous Energy Spectrum

Continuous Beta Energy Spectrum

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Gamma Radioactivity

• Gamma radioactivity iscomposed of electromagneticrays. It is distinguished from x-rays only by the fact that itcomes from the nucleus. Mostgamma rays are higher inenergy than x-rays and

therefore are very penetrating.

AZX* A

ZX 0 0

Discrete Energy Spectrum

Gamma Emissions

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Electromagnetic Spectrum

Electron Capture

• Electron capture is one form of radioactivity. Aparent nucleus may capture one of its orbitalelectrons and emit a neutrino This is a processelectrons and emit a neutrino. This is a processwhich competes with positron emission and has thesame effect on the atomic number. Most commonly,it is a K-shell electron which is captured, and this isreferred to as K-capture.

• A typical example is:

Q = (MX + Me MY)c2 0

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Internal Conversion

137Cs Decay

Isomeric State

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60Co Decay

1.33 MeV

1.17 MeV

238U Decay Series

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235U Decay Series

232Th Decay Series

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237Np Decay Series