Carbon dating works by measuring the ratio of carbon-14 to carbon-12 in organic material. Over time, the amount of carbon-14 decreases as it radioactively decays. By measuring the current ratio and knowing the half-life, the age of once-living material can be estimated. However, the production rate of carbon-14 in the atmosphere may change in the future due to factors like solar activity or human activity like nuclear weapons testing. This could affect the accuracy of carbon dating beyond about 50,000 years ago.

1. Nuclear Physics
An introduction
Brief history
Binding energy
Semi empirical mass formula or the Liquid drop
model
Radioactivity
Nuclear energy & some applications

2. 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 stardust
 Applications are plenty
◦ Energy (Fission, fusion, transmutation)
◦ Medicine (Radiotherapy, MRI)
◦ Instrumentation (e.g. spectroscopy)
◦ Devices (e.g. Smoke detector)
◦ Radioactive dating

3. Brief history
 1896 Becquerel - radioactivity
 1897 Thomson - electron
 1898 Curies – radium
 1911 Rutherford – nucleus
 1932 Chadwick - neutron

4. Dimensions

5. 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
A
Z EN
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

6. Basic properties
 Size
◦ Most nuclei are nearly spherical, with the radius being
given by1/3 fm
R 1.2 A
 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
BE Z M H N M N M ( A, Z ) c2
◦ The difference is known as the binding energy and is
given by

7. Nuclear binding energy

8. 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

9. Liquid drop model
Bethe-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 term
Bulk binding energy volume EV aV A
Ev R3
= (r0 A1/3)3

10. Surface term
Surface area = 4 r 2 4 (r0 A 1/ 3 )2 4 r02 A 2/ 3
Surface energy aS A 2/ 3
Coulomb term
The work done to bring together Z protons from infinity
e
V
4 0r
For Z ( Z 1) / 2 pairs of protons
Z ( Z 1) Z ( Z 1)e2 1
EC V
2 8 0 r AV
1/ 3 Z ( Z 1)
r A EC aC
A1/ 3

11. Asymmetry term
 Neutron and proton states with
Neutrons Protons 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 N Z
excess protons over neutrons the
extra energy is [(N Z)/2]2 .
relative to Z = N.
(N Z )2
E Asym aa
A  1/A

12. Pairing term
 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)
BE (even-Z , odd-N )
BE (even-Z , even-N ) BE (odd-Z , odd-N )
BE (odd-Z , even-N )
= +ve 0 -ve
 Its observed that this effect smaller for larger A
 Phenomenological fit to A dependence  EPair 1/A1/3
E Pair ap 1/ 3
A

13. e=even o=odd
+ 33.5 MeV (e-e)
ap= 0 MeV (o-e or e-o)
av=14.1 MeV ac=0.595 MeV - 33.5 MeV (o-o)
2 2
2
3
Z (N Z )
EBind av A as A ac 1
aa ap 1/ 3
A 3 A A
as=13.0 MeV aa=19.0 MeV
BE ( N , Z )
Constraint for most stable isotope
N Z Const.

14. #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);
}
}

15. 15
10
Volume Surface
BE/A (MeV)
5
Coulomb Asymmetry
Pairing Total
0
-5
-10
0 50 100 150 200 250
A

17. 200
180
160
140
120
Protons
N=Z
100
80
60
beta stability
40
20
0
0 50 100 150
Neutrons

18. SHE – discovery in nuclear labs

19. The Chart of Nuclides

20. Present scenario
2900 nuclei till year 2000
3090 till August 2008
3000 more to be discovered

21. Classification of Decays
-decay:
• emission of Helium nucleus
• ZZ-2
Protons
• NN-2
• AA-4
EC --decay
• emission of e- and
• ZZ+1
• NN-1
• A=const
+-decay
• emission of e+ and
• ZZ-1
• NN+1
Neutrons • A=const
Electron Capture (EC)
• absorbtion of e- and emiss
-decay • ZZ-1
• emission of • NN+1
• Z,N,A all const • A=const 21

22. Spin 1 1 3
S s( s 1)  1  
2 2 2
1
ms
2
Magnetic Moment
e 27
Nuclear magneton N 5.051 10 J/T
2m p
 
Proton pz 2.793 N pz has same direction as S
 
Neutron nz  1.913 N nz is opposite to S
Magnetic energy U m z B, E 2 z B
Nuclear Zeeman effect

23. 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.

24. 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…

25. 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).

26. 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?