A&n Structure 3

7/27/2019 A&n Structure 3

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Atomic & Nuclear Structure

F. Z. Khiar i

Physics Department

King Fahd University of Petroleum & Minerals

Dhahran, Saudi Arabia


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The Elements


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Atoms and Elements

Ordinary matter is composed of atoms. An atom consistsof a tiny nucleus made up of protons and neutrons, on

the order of 20,000 times smaller than the size of the

atom. The outer part of the atom consists of a number of

electrons equal to the number of protons, making thenormal atom electrically neutral.


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A very simplisticvisualization of anatom includes a densenucleus comprised of a

specific number ofpositively chargedprotons and unchargedneutrons surrounded by

orbits of negativelycharged electrons


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Relative scale model of an atom

and the solar system


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Quantized Energy States

The electrons in free atoms can be found in only certaindiscrete energy states. These sharp energy states are

associated with the orbits or shells of electrons in an atom,

e.g., a hydrogen atom.

One of the implications of these quantized energy states is

that only certain photon energies are allowed when

electrons jump down from higher levels to lower levels,

producing the hydrogen spectrum.


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Quantized Energy States


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Atomic Radii


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Nuclear Notation

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


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Isotopes

The different isotopes of a given element have the sameatomic number but different mass numbers since theyhave different numbers of neutrons. The chemical

properties of the different isotopes of an element areidentical, but they will often have great differences in

nuclear stability.

For stable isotopes of light elements, the number ofneutrons will be almost equal to the number of protons,

but a growing neutron excess is characteristic of stable

heavy elements. The elementtin(Sn) has the most stableisotopes with 10, the average being about 2.6 stableisotopes per element


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Isotopes


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Z Isotope Mass

Number

Atomic Mass

of Isotope

Abundance

[%]

Atomic Mass

of Element1 H

DT

1

23

1.0078250321

2.01410177803.0160492675

99.9885

0.0115

1.00794

2 He 3

4

3.016029309 7

4.0026032497

0.000137

99.999863

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 1213

14

12.000000013.0033548378

14.003241988

98.931.07

12.0107

7 N 1415

14.003 074005215.0001088984

99.6320.368

14.0067

8 O 16

1718

15.9949146221

16.9991315017.9991604

99.757

0.0380.205

15.9994


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Nuclear Units

Nuclear energies are very high compared toatomic processes, and need larger units


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Nuclear Units

Nuclear sizes are quite small and needsmaller units:


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Nuclear Units

Nuclear masses are measured in terms of atomic massunits (amu, u) with the carbon-12 nucleus defined ashaving a mass of exactly 12 amu. It is also common

practice to quote the rest mass energy E = mc2 as if itwere the mass. The conversion to amu is:


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The Mole

A mole (abbreviated mol) of a pure substanceis a mass of the material in grams which isnumerically equal to the molecular mass. Amole of any material will contain Avogadro'snumber of molecules. For example, carbon hasan atomic mass of exactly 12.0 atomic massunits -- a mole of carbon is therefore 12 grams.


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Constituents of Atoms

The electrons,protons and

neutronswhich makeup an atomhave definite

charges andmasses.


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Constituents of Atoms

While the charges and masses are precisely known,the sizing is not. Our best information about the

proton and neutron indicates that they are constituent

particles. However we can attribute to them a radiusof about

1.2 x 10-15 meters = 1.2 fm

The electron is a fundamental particle which isapparently not made out of any constituent particles.


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Nuclear Forces

Within the incrediblysmall nuclear size, thetwo strongest forces innature are pittedagainst each other.

When the balance isbroken, the resultantradioactivity yields

particles of enormousenergy.


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Nuclear Forces

The electron in a hydrogen atom is attracted tothe proton nucleus with an electromagneticforce so strong that gravity is negligible bycomparison. But two protons touching each

other would feel a repulsive force over 100million times stronger!! So how can suchprotons stay in such close proximity? This maygive you some feeling for the enormity of the

nuclear strong force which holds the nucleitogether

N l Si d D i


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Nuclear Size and Density

Various types of scattering experiments suggestthat nuclei are roughly spherical and appear to

have essentially the same density.

Nuclear Density &


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Nuclear Density &

The Strong Nuclear Force

The fact that the nuclear density seems tobe independent of the details of neutron

number or proton number implies that the

force between the particles is essentiallythe same whether they are protons or

neutrons. This correlates with other

evidence that the strong force is the same

between any pair of nucleons


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Nuclear Binding Energy

Nuclei are made up of protons and neutron, but themass of a nucleus is always less than the sum of theindividual masses of the protons and neutrons whichconstitute it. The difference is a measure of the nuclear

binding energy which holds the nucleus together. This

binding energy can be calculated from the Energy -Mass relationship:

Nuclear Binding Energy: BE = Dmc2

Dm = Z.mp + N.mnM(A,Z)


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For the alpha particle Dm = 0.0304 u whichgives a binding energy of28.3 MeV


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The binding energies of nucleons are inthe range of millions of eV compared to

tens of eV for atomic electrons.

Whereas an atomic transition might emit a

photon in the range of a few electron volts,

nuclear transitions can emit gamma-rayswith quantum energies in the MeV range


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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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Nuclear Binding Energy Curve

The fact that there is a peak in the binding

energy curve in the region of stability near

iron means that either the break up of

heavier nuclei (fission) or the combiningof lighter nuclei (fusion) will yield nuclei

which are more tightly bound (less mass

per nucleon).

Fi i


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Fission

X + n fission Y* + Z* + neutrons

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

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

E = DMc2

Fi i F t


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Fission Fragments

When 235U undergoes

fission, the average of the

fragment mass is about 118,

but very few fragments nearthat average are found. It is

much more probable to break

up into unequal fragments,

and the most probablefragment masses are around

mass 95 and 137.


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Uranium Fission

i


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Fusion

X + Y fusion Z + nucleon

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

DM = M(X) + M(Y)M(Z)M(nucleon)

E = DMc2


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Proton-Proton Fusion

This is the nuclear fusion process which fuels the Sun and other

stars which have core temperatures less than 15 million Kelvin. Areaction cycle yields about 25 MeV of energy

D t i T iti F i


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Deuterium-Tritium Fusion

For potential nuclear energy sources for the Earth, thedeuterium-tritium fusion reaction contained by somekind of magnetic confinement seems the most likely

path.

The reaction yields 17.6 MeV of energy but requires atemperature of approximately 40 million Kelvins toovercome the coulomb barrier and ignite it. Thedeuterium fuel is abundant, but tritium must be either

bred from lithium or gotten in 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 Avogadros NumberNA


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Questions ?

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A&n Structure 3