Sri Ramakrishna College of Arts & Science, Coimbatore, Department of Physics.

1. Nuclear
Physics
Unit V

2. Introduction
• Z – Atomic Number – Number of Protons
• A – Mass Number – Number of Nucleons
• Species of nucleus – Nuclide - 𝑧𝑋𝐴
• N – Number of neutrons = A-Z

3. Classification of Atomic Nuclei
• Isotopes – Same ‘Z’ , different ‘A’ – Same Chemical Prop and Different Physics
Prop - 14𝑆28 , 14𝑆29 , 14𝑆30
• Isobars – Same ‘A’ , different ‘Z’ – Different Physics & Chemical Prop - 8𝑂16 ,
7𝑁16
• Isotones – Equal number of neutrons - 8𝑂16 , 7𝑁15 - (N=8)
• Isomers – Same ‘Z’ and ‘A’ – Different nuclear energy states and internal
structure
• Mirror Nuclei – Same Mass Number with proton and neutron number
interchanged - 8𝑂15 , 7𝑁15 - (For Oxygen – Z=8 & N=7; Nitrogen – Z=7 & N=8)

4. General Properties of Nucleus
• Nuclear Size : 𝑅 = 𝑟0𝐴1 3
• Nuclear Mass :
• Assumed Mass = Zmp + Nmn
• Real Mass < Zmp + Nmn
• Assumed Mass – Real Mass = Δ𝑚 Mass Defect
• Nuclear Density : 𝜌𝑁 =
𝑁𝑢𝑐𝑙𝑒𝑎𝑟 𝑀𝑎𝑠𝑠
𝑁𝑢𝑐𝑙𝑒𝑎𝑟 𝑉𝑜𝑙𝑢𝑚𝑒
=
𝐴𝑚𝑁
4
3
𝜋𝑟0
3𝐴
=
𝑚𝑁
4
3
𝜋𝑟0
3
= 1.816 𝑋 1017 𝐾𝑔 /𝑚3
• Nuclear Charge : Ze

5. Models of Nuclear Structure
• The Liquid Drop Model
• Shell Model
• Collective Model

6. The Liquid Drop Model
• Neils Bohr Proposed
I. Nucleus supposed to be Spherical in shape – Symmetrical Surface Tension
II. Force of ST – surface of liquid drop; Potential barrier at the surface of nucleus
III. Density of LD – independent of its Volume; Density of Nucleus – Independent of
its Volume
IV. Intermolecular forces – Short Range
V. Raised Temperature – molecules evaporates in LD; bombarding – compound
nucleus with emitting nuclear radiation
VI. LD – oscillate – two smaller drops; Fission is similar

7. Semi Empirical Mass Formula
• Binding Energy – BE = 𝑎𝐴 − 𝑏𝐴
1
3 −
𝐶𝑍 Z−1
𝐴1 3 −
𝑑𝑍 (N−𝑍) 2
𝐴
±
𝛿
𝐴
3
4

8. Shell Model
• Energy level of nucleons – Similar to electron shells in an atom
• Proton and Neutron are grouped in shells in nucleus
• Shells – Filled – specific number of proton/neutron/both
• Number of nucleons in each shell is limited by Pauli’s Exclusion Principle
• Shell Model – Independent Particle Model

9. Evidence for Shell Model
• Nucleus is stable if it contains certain number of Proton/Neutron – Magic
numbers – 2,8,20,50,82 & 126
• Inert gasses – closed electron shell – highly stable
• Isotopes – isotopic abundance > 60% - magic number category
• Tin – (50Sn) has ten Isotopes; Calcium – (20Cs40) has six stable isotopes. ie
elements with Z=50,20 are more stable.
• Radioactive series – Uranium, Actinium, Thorium – decay to 82Pb208 – stable
• Magic number nuclei – cannot accept extra – Shells are closed
• Spontaneous neutron emission 8O17, 36Kr87, 54Xe137 N = 8+1, 50+1, 82+1

10. Experimentally Confirmed Results
• Even – Even Nuclei are more stable than Odd – Odd Nuclei
• Able to Predict Total Angular Momenta of Nuclei
• Even – Even = Zero
• Odd – Even = half-integral total angular momenta
• Odd – Odd = Integral Total Angular momenta

11. Collective Model
• Proposed by A.Bohr, B.R. Mottleson, James Rainwater.
• Combines the best features of Liquid Drop and Shell Models
• Nucleons exert centrifugal force on the surface of nucleus – permanent deformation
to non – spherical shape – surface may undergo periodic oscillations
• Drop like properties – Fission
• Retains shell model characteristics
• 𝑊 = 𝐸𝑟𝑜𝑡 + 𝐸𝑣𝑖𝑏 + 𝐸𝑛
• Even – Even Nuclei – Spherical Shape, Zero Quadrupole Moment;
• Odd-Odd , Odd-Even, Even –Odd = Non-spherical Shape, Finite Quadrupole
Moment

12. Interaction between Energetic
Particles and Matter
• Heavy Charged Particle
• Electrons
• The Absorption of 𝛾 – Rays
• Photoelectric effect
• Pair production
• Compton effect

13. Ionization Chamber
• Charged subatomic particles can ionize gases
• Number of ion pairs produced – info about nature of incident particle and
their energy

14. Ionization Chamber
• C – Hollow Cylinder
• W –Window
• R – Metal Rod
• E – Quandrant Electrometer
• G – Earthed Guard ring
• C – Contains sulphur dioxide / methyl bromide
• Ionization current produced – 10-12 to 10-15 Amperes
• Pulse amplifier – measures individual particles

15. Ionization chamber
• Study alpha particles, beta particles, protons, electrons and nuclei

16. Proportional
Counter
• A proportional counter, also
known as the proportional
detector, is an electrical
device that detects various
types of ionizing radiation.
• Cylinder – Anode – 2 cm dia
• Central wire – 10micro-m dia
– 20cm length

17. Proportional Counter
• Pulse size α number of ion pairs – hence proportional counter
• 𝐸 =
𝑉
𝑟 log𝑒 𝑏 𝑎
• b – radius of the cylinder
• a – radius of the wire
• r – distance from center where E is measured
• V – positive voltage pf the central wire

18. Proportional
Counter
• Pulse size α number of
ion pairs – hence
proportional counter
•𝐸 =
𝑉
𝑟 log𝑒 𝑏 𝑎
• b – radius of the cylinder
• a – radius of the wire
• r – distance from center where E is
measured
• V – positive voltage pf the central
wire

19. GM Counter

20. Elementary Particles

21. Particles and Anti Particles

22. The Fundamental Interactions

23. The Fundamental Interactions
Interaction
Particle
affected
Range
Relative
Strength
Particles
Exchanged
Strong Hardons 10-15 m 1 Mesons
Electromagnetic
Charged
Particles
Infinity 10-2 Photons
Weak
Hardons &
Leptons
10-17 m 10-13 Intermediate
bosons
Gravitational All Infinity 10-40 Gravitons