General Properties of Nuclear

CHAPTER 1 - General Properties of Nuclear

1. CHAPTER 1
GENERAL PROPERTIES OF NUCLEAR

2. INTRODUCTION
►Origins of nuclear physics;
►1896 – Henri Becquerel discovered photographic plates fogged by unknown radiation
– emanating from uranium ores.



►Extensively studied by Pierre & Marie Curie, and Ernest Rutherford and his
collaborators – found 3 types of radiation : α, ß and γ rays.

Radioactivity : some
nuclei are unstable and
spontaneously decay
Bound states of 2 protons & 2
neutrons
Electrons
Photons – Quanta of
electromagnetic radiation
Henri Becquerel
Pierre & Marie Curie

3. Jean Baptiste
Perrin
Study radiation occur
when electric field
established between
electrodes in an
evacuated glass tube.
J. J. Thomson
1897 - Establish the
nature of the radiation
(cathode rays), free
electrons, e
-
> measure
mass and charge.

4. ►Support the stability of atoms
►Cannot explain the discrete wavelengths observed in
the light spectra emitted by excited atoms.
►1911 - Rutherford’s experiment;

►Alpha particles bombarded to a thin gold foil.
►Expected : Most of the particles pass through the thin
foil, some deflected with small angles.
►Findings : There are particles scattered at very large
angles, > 90˚.
►Particles encounter a very small positively charged
central nucleus.

5. ►Atoms like a “planetary system”
►Nucleus – Center
►Electrons – Orbits surrounding the nucleus

►Discrete wavelength of light spectra –
movement of electrons between the
orbits


Ernest Rutherford
> Heavier atom
has nuclei
consists of
several
protons.
Nitrogen atom

6. ►Concept of isotopism;
►Isotopes – Atoms that have nuclei with different mass, but similar charges.






►Irene Curie & Frederic Joliot – bombarded α-particles to beryllium (Be), neutral radiation was
emitted – exposed to paraffin, energy of protons released was studied.
►1932 – Chadwick implies the existence of an electrically neutral particle (neutron), same mass as
proton.
Protons + Neutrons
Nucleons – Binding interaction
called as strong nuclear force

7. 1.1 RUTHERFORD SCATTERING
►Finding not compatible with scattering from light particles such as
electrons.
►Ignoring Coulomb interaction, consider the non-relativistic elastic
scattering;




►Conservation of linear momentum and kinetic energy,






There are particles scattered
at very large angles, > 90˚.

Momentum
Kinetic EnergyEq.2
Eq.1

8. ►Squaring E.q 1, we obtained;


►E.q 3 = E.q 2;



Eq.3
m
t
= m
e
<< m
α
, will
become +ve ~ v
t
and v
f
+ve (particles moving
essentially along the
initial direction)
m
t
= m
Au
<< m
α
, will
become -ve ~ v
t
and v
f

-ve (large scattering
angle possible)
Might be due to multiple small-angle
scattering > rules out by thin gold foil
v +ve
v -ve

9. ►Taking account of Coulomb interaction, use the non-relativistic classical
mechanics;






►Conservation of angular and linear momentum,


►Initial linear momentum,

►Final linear momentum,
Interaction between charges, similar charges
repels, opposite charges attracts
< Target mass assumed to be large that its recoil is neglected.
< Initial velocity, v
< Absence of any interaction, particle moves in a straight line
and pass the target at a distance b (impact parameter).
> Change in momentum,

10. ►Let ;



►If initial flux of α-particles is J;
►Intensity of particles having impact parameter b + db = 2πb Jdb

Rate of particles scattered into a
solid angle dΩ = 2π sin θ dθ
i
ii
i = ii Subs. b
> Final form of Rutherford differential
cross-section for non-relativistic scattering

11. Conclusions from
Rutherford scattering
►General properties of nucleus;
►The mass of an atom is
concentrated in the nucleus.
►Most of the space in an atom is
empty.
►The nucleus occupied a very
small volume of an atom.
►Some positively charged region
(the nucleus) is responsible for
the large deflection angle of the
alpha particles.

12. 1.2 CHARGE AND MASS DISTRIBUTION OF
THE NUCLEUS
►Measurement carried out since the middle 1950’s.
►Nuclei - spheres with diffuse surfaces.
►Interior – charge density nearly constant.
►Surface – charge density falls over relatively large
range.


►Where c = radius at which ρ(r) reduces by one half
►For large nuclei,
> Radial charge distributions of various nuclei.

13. ►Mean square radius can be calculated;

►Relation between R and r
2
;


►In terms of atomic mass, A;

►Surface thickness, t;

►For heavy nuclei, the value is roughly,


R
Nucleus always approximated as
homogeneously charged sphere

14. ► 

15. 1.3 COMPOSITION OF THE NUCLEUS
►Z = Atomic number (sometimes called charge number), equal to number
of protons
►N = Neutron number
►A = Mass number, equal to number of nucleons (Z + N)
►Isotopes have same Z, different A and N
►Natural abundances different between one isotope to another.
►Also can be produced in the laboratory by nuclear reactions.
NuclideDef: Each nuclear
species with a given Z
and A

16. ►Isotones – same N, different A and Z
►Isobars – same A, different N and Z








►Why electrons cannot exist in nucleus?
►Nuclear size – Uncertainty principle put a lower limit in its kinetic energy, much larger than kinetic energy
observed when electron emitted from nuclei.
►Nuclear spin – The nuclear spin if electron exists in the nucleus is not similar to the measured nuclear spin.
►Nuclear magnetic moment – The measured magnetic moment is in the same order of magnitude of the proton’s.

17. Up quarks Top quarks
Bottom quarks Charm quarks
Strange quarks
Down quarks

18. 1.4 NUCLEAR BINDING ENERGY
►Nucleus binds together by nuclear force.







►Neutrons help in holding a nucleus together.
►2 nucleons within about 2 fm to one another – feel an attractive force.
►Inter-nucleon potential
► has a “hard-core” – prevents nucleons to be closer than 0.4 fm.
►Independent of their charge.
►Nuclear force : short range – falls to zero abruptly with inter-particle separation = Stable

19. ►Nuclear force
►Works best if the nucleus is not too large.
►Should balance with electrostatic repulsion force of protons.
►Nucleus larger, more neutrons needed to counteract the repulsion force between protons.
►Some combinations make a stable nucleus, some are not – causes the atom to decay.

20. ►Nuclear force – contribute to the total mass of an atom M(Z,A)


►Where M
p
= mass of proton, m
e
= mass of electron, M
n
= mass of neutron
►The mass deficit, ΔM (Z,A);


►Binding energy,
►Energy required to separate nucleus into its constituents.
►Energy released when a nucleus formed from its constituent particles.
►ΔE
be
= -ΔMc
2

►A measure of stability of an atom;
►High ΔE
be
, high stability
►Lightest and heaviest elements – low ΔE
be

►Intermediate elements – highest ΔE
be


 

21. ►Binding energy per nucleon, ΔE
ben

►Def: Average energy holding each nucleon into nucleus.

> Curve increases rapidly, demonstrate
the saturation effect of nuclear force.

22. Example
► 

23. Exercises
► 

24. PAST YEAR QUESTIONS
►DEC2019, Q1.a)ii,iii, b)
►JUN2019, Q1.b)
►JUL2017, Q1.a)
►DEC2016, Q1.b)