Download - nuclear physics
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Nuclear PhysicsAn introduction
Brief historyBinding energySemi empirical mass formula or the Liquid drop modelRadioactivityNuclear energy & some applications
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Why Study Nuclear Physics?To understand origin of different nuclei
◦ Big bang: H, He and Li◦ Stars: elements up to Fe◦ Supernova: heavy elements
We are all made of stardustApplications are plenty
◦ Energy (Fission, fusion, transmutation)◦ Medicine (Radiotherapy, MRI)◦ Instrumentation (e.g. spectroscopy)◦ Devices (e.g. Smoke detector)◦ Radioactive dating
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Brief history1896 Becquerel - radioactivity1897 Thomson - electron1898 Curies – radium1911 Rutherford – nucleus1932 Chadwick - neutron
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Dimensions
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Basics The number of protons inside the nucleus is
designated by Z and is known as the Atomic Number
The number of neutrons inside the nucleus is designated by N and is known as the Neutron Number
The mass number, A, is the sum of the atomic number and the neutron number A = Z + N
The mass number is an integer and is only approximately equal to the atomic weight of a element
A nuclide is a single nuclear species having a specific Z and N. The notation that is used to designate the nuclides is
Nuclei with same Z, but differing N Isotopes
Nuclei with same N, but differing Z Isotones
Nuclei with same A Isobars
Nuclei with longer lifetime in an excited state Isomers
AZ NE
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Basic propertiesSize
◦ Most nuclei are nearly spherical, with the radius being given by
Density◦ The nucleus has approximately constant density
~ 1017 kg/m3
Binding energy◦ When you measure the mass of an atom you find
that it is less than the sum of its parts◦ The difference is known as the binding energy
and is given by
◦ Measure relative masses by energy released in decays or reactions: X Y + Z + DE
◦ Mass difference between X and Y+Z is DE/c2.
1/31.2 fmR A
2( , ) H NBE Z M N M M A Z c
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Nuclear binding energy
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Models of the nucleus
No fundamental theory that can explain all observed properties of the nucleus exists
Several models developed to explain some of the observed properties
Liquid Drop Model–Nucleons are treated as molecules in a liquid
Shell Model–Similar to central field approximation in atomic structure
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Liquid drop modelBethe-Wiezsacker mass formula (1935)Assumptions
Each nucleon in interacting solely with its nearest neighbours
Equivalent to atoms in a solid or molecules in liquid which move freely while maintaining fixed intermolecular distance
Vibrations in solid would be too high for stability
Nucleus ~ charged liquid drop
We may consider different effects term-wise
Volume termBulk binding energy volume
Ev R3
= (r0 A1/3)3
V VE a A
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Surface term
Coulomb termThe work done to bring together Z protons from infinity
2Surface area = 4 r 1/ 3 204 ( )r A 2 2/ 3
04 r A
2/ 3Surface energy Sa A
04e
Vr
For ( 1)/ 2 pairs of protonsZ Z ( 1)
2C
Z ZE V
2
0
( 1) 18 AV
Z Z er
1/ 31/ 3
( 1)C C
Z Zr A E a
A
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Neutron and proton states with same spacing .
Crosses represent initially occupied states in ground state.
If three protons were turned into neutrons the extra energy required would be 3×3 .
In general if there are NZ excess protons over neutrons the extra energy is [(N Z)/2]2 . relative to Z = N.
1/A
Asymmetry term
2( )Asym a
N ZE a
A
Neutrons Protons
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Like Cooper pair formation, the nucleons also can pair
Some energy is spent in binding the pairs
BE(Nucleus with paired nucleons) > BE(Nucleus with unpaired nucleons)
Its observed that this effect smaller for larger A
Phenomenological fit to A dependence EPair 1/A1/3
(even- ,odd- )(even- ,even- ) (odd- ,odd- )
(odd- ,even- )
BE Z NBE Z N BE Z N
BE Z N
Pairing term
1/ 3Pair pE aA
= +ve 0 -ve
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3/1
2
31
23
2 )(
Aa
A
ZNa
A
ZaAaAaE pacsvBind
av=14.1 MeV ac=0.595 MeV
as=13.0 MeV aa=19.0 MeV
e=even o=odd
+ 33.5 MeV (e-e)
ap= 0 MeV (o-e or e-o)
- 33.5 MeV (o-o)
Const.
( , )Constraint for most stable isotope
Z
BE N ZN
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#include<stdio.h>#include<math.h>#include<string.h>FILE *fout1;main(){int iA,iZ;float A,Z,del;float VEP,SEP,CEP,AEP,PEP,BEP;float av=14.1,as=13.0,ac=0.595,aa=19.0,ap=33.5;fout1=fopen("BEP.OUT","w");fprintf(fout1," Z A VEP SEP CEP AEP PEP BEP");for (iA=1;iA<=300;iA++) {A=(float)(iA); Z=0.5*A/(1.0+pow(A,2.0/3.0)*ac/(4.0*aa)); iZ=(int)(Z); Z=(float)(iZ); printf("\n%f %f",Z,A); VEP=av; SEP=-as/pow(A,1.0/3.0); CEP=-ac*Z*Z/pow(A,4.0/3.0); AEP=-aa*pow((A-2*Z)/A,2); if(iA%2 != 0) del=0; else { if(iZ%2 != 0) del=-1; else del=1; } PEP=ap*del/pow(A,4.0/3.0); BEP=VEP+SEP+CEP+AEP+PEP; fprintf(fout1,"\n%10.4f%10.4f%10.4f%10.4f%10.4f%10.4f%10.4f%10.4f",Z,A,VEP,SEP,CEP,AEP,PEP,BEP); }}
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-10
-5
0
5
10
15
0 50 100 150 200 250
A
BE
/A (
MeV
) Volume Surface
Coulomb AsymmetryPairing Total
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0
20
40
60
80
100
120
140
160
180
200
0 50 100 150
Neutrons
Protons N=Z
beta stability
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SHE – discovery in nuclear labs
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The Chart of Nuclides
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Present scenario
2900 nuclei till year 20003090 till August 20083000 more to be discovered
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21
Classification of Decays
Neutrons
Pro
ton
s
a
b-
a-decay: • emission of Helium nucleus• ZZ-2• NN-2• AA-4
b--decay• emission of e- and n• ZZ+1• NN-1• A=const
g-decay• emission of g• Z,N,A all const
b+-decay• emission of e+ and n• ZZ-1• NN+1• A=const
b+EC
Electron Capture (EC)• absorbtion of e- and emiss
n• ZZ-1• NN+1• A=const
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Spin
2
1
2
31
2
1
2
1)1(
sm
ssS
Magnetic Moment
BEBU
S
S
m
e
zzm
nzNnz
pzNpz
pN
2,energy Magnetic
toopposite is 913.1Neutron
asdirection same has 793.2Proton
J/T10051.52
magneton Nuclear 27
Nuclear Zeeman effect
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Practical Applications
Nuclear fission for energy generation.◦ No greenhouse gasses◦ Safety and storage of radioactive material.
Nuclear fusion◦ No safety issue (not a bomb)◦ Less radioactive material but still some
technical difficulties.
Nuclear transmutation of radioactive waste with neutrons.◦ Turn long lived isotopes stable or short lived.
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Medical Applications
Radiotherapy for cancer◦ Kill cancer cells.◦ Used for 100 years but can be improved by
better delivery and dosimetery◦ Heavy ion beams can give more localised
energy deposition.
Medical Imaging◦ MRI (Nuclear magnetic resonance)◦ X-rays (better detectors lower doses)◦ Many others…
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Other Applications
Radioactive Dating◦C14/C12 gives ages for dead
plants/animals/people.◦ Rb/Sr gives age of earth as 4.5 Gyr.
Element analysis◦Forenesic (eg date As in hair).◦Biology (eg elements in blood cells)◦Archaeology (eg provenance via
isotope ratios).
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Carbon Dating
C14 produced by Cosmic rays (mainly neutrons) at the top of the atmosphere.◦ n N14 p C14
C14 mixes in atmosphere and absorbed by plants/trees constant ratio C14 / C12 . Ratio decreases when plant dies. t1/2=5700 years.
Either◦ Rate of C14 radioactive decays◦ Count C14 atoms in sample by Accelerator Mass
Spectrometer.Which is better?Why won’t this work in the future?