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