PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Lecture course slides can be seen at:
•  http://www.star.le.ac.uk/~mbu/
lectures.html
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Ch. 40
Nuclear size and Shape
•  Nuclei exist bcse strong nuclear force overcomes
electrostatic repulsion force over close distances
inside nucleus
•  Energetics & stability of nucleus depends on
number of protons & electrons inside
Z, the number of protons, the atomic
number of the atom.
N, the number of neutrons.
A, the mass number of the nucleus, the
total number of nucleons, A=N+Z.
From scattering experiments, nuclei are
roughly spherical with radius proportional to
number of nucleons A1/3
R = R0 A1/3
where R0=1.2-1.5 femtometres = 1.2-1.5x10-15m
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Ch. 40
Nuclear size and Shape
R = R0 A1/3
• 
• 
• 
• 
Volume is proportional to A, so density constant
Nucleus looks like a liquid drop
For light nuclei N~Z
For heavier nuclei the number of neutrons
increases
•  The extra uncharged neutrons act to stabilize heavy
nuclei from repulsive electrostatic forces
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Nuclear density
Estimate the density of nuclear matter.
Density:
! = M /V =
M
4"
( )R03 A
3
M = mass of proton/neutron = 1.67x10-27kg x A
R0= 1.5x10-15m
Find density = 1.18x1017kg m-3
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Ch. 40
The radioactive decay process
β-Decay:
either a neutron turns into a proton, with emission of an
electron (β-) or proton turns into a neutron (β+):
14
6
14
7
"
C ! N + e +!e
13
7
N ! 136 C + e+ + ! e
So A remains same, Z changes by +/-1
γ-Decay:
excited nucleus decays into lower energy state via emission
of a photon. A and Z constant
α-Decay:
tends to occur in heavier elements, which can become more
stable by reducing their size
232
90
228
T ! 228
Ra
+
!
=
88
88 Ra + He
N and Z decrease by 2, A decreases by 4
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Ch. 40
Mass and binding energy
•  Binding energy per nucleon
varies with mass number A
•  For small A (<50)
• 
• 
Steady increase in number of
nearest neighbours as A increases
Therefore an increase in no. of
bonds per nucleon
•  For medium A (>50) curve ~flat
• 
• 
• 
Additional nucleons too far away
Nuclear forces saturate
Only nearest neighbours important
•  For large A (>200)
• 
• 
Coulomb repulsion force becomes
large
Nucleus unstable, spontaneous
fission
•  Fusion of nuclei to the left of Fe
•  Fission to the right
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Ch. 40
Mass and binding energy
•  This plot of mass difference
per nucleon v A is the negative
of the binding energy curve
•  The rest mass per nucleon for
both very heavy (A>200) and
very light (A<20) nuclides is
more than for nuclides of
intermediate mass
•  Thus, energy is released when
a very heavy nucleus breaks
up into two lighter nuclei
(fission)
•  Or when two light nuclei fuse
together to form a heavier
nucleus (fusion)
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Fission
•  Very heavy nuclei can spontaneously break apart,
placing limit on size of nucleus and number of
possible elements
•  Some heavy elements can be induced to fission by
capture of a neutron
•  Fission of 235U (right):
•  Nucleus excited by capture of neutron
•  Splits into two daughter nuclei & emits more
neutrons (avg 2.5)
•  Coulomb repulsion force drives fragments
apart
•  Thermal energy released (exothermic)
•  Self-sustaining reaction (chain reaction)
possible
•  Big bang with nasty isotopes
•  Or control in reactor by keeping number of
viable neutrons per reaction to 1
n + 235U ! 141Ba + 92 Kr + 3n
PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei
Fusion
2
H + 3 H ! 4 He + n +17.6MeV
•  Two light nuclei fuse to form a heavier nucleus
•  Energy per unit mass > fission
•  Abundance of light elements holds great promise for producing power from
fusion
•  Fewer dangers than fission (chain reactions, nasty isotopes)
•  Bcse of coulomb repulsion, kinetic energies ~1MeV needed to get deuterium
and tritium close enough for nuclear forces to become effective & fusion to
occur
•  Scattering more likely
•  Particles must be heated to high enough temps (~108K) for fusion to occur as
a result of thermal collisions
•  Temps like this found in stars
•  At this temp, gas is a plasma of +ve ions and e•  Confining plasma difficult
•  Done by star’s high gravity
•  Barely achieved in any fusion reactor to date