Nuclear Physics

1
Nuclear Physics

• Micro-world Macro-world
• Lecture 16

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Neutron
By 1930, the charge and masses of many
different nuclei were known. The charges were
found to be Qnucleus Z x proton charge the
masses were Mnucleus A x proton mass Z is
always an integer A is nearly an integer But,
except for hydrogen where AZ1, A Z are
different.
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Electrons in the nucleus?
One idea was that the nucleus contained A
protons and A-Z electrons. But Heisenbergs
uncertainty principle forbids this
Suppose Dx 1x10-14m
typical size of a nucleus
6.6x10-34Js 1x10-14m
Dpx gt
6.6x10-28kgm/s
non-relativistic calculation is invalid
Dpx me
6.6x10-28Js 9x10-31kg

Dvx gt
gtspeed of light
Correct calculation gives Eelectron gt 2x106
eV, such electrons would not stay inside a nucleus
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Discovery of the neutron
source
detector
James Chadwick
Po
detector
a
Be
n
No electric charge mass proton mass
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Nucleons (protons neutrons)

proton neutron
mass 1.672x10-27kg 1.675x10-27kg mc2
938.27 MeV 939.57 MeV Charge
1.6x10-19 C 0
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Isotopes
Same chemistry very different nuclear physics
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Light isotopes
A number of protons neutrons
AX
Z
Z of protons
Chemical symbol
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All elements have isotopes
235
238
U
U
92
92
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Nuclear force
The very powerful electrical repulsion (100s
of Newtons) must be counteracted by some other
very strong attractive force


This new force is called the Strong Nuclear force
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Strong Nuclear force
repulsive electrical force
Force
repulsion is stronger here
attraction is stronger here
Attractive nuclear force
1.0 2.0 3.0 4.0 5.0
Distance (x10-15m)
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Strong Nuclear Force

• It is very strong
• It overcomes the electrical repulsion between
  positively charged protons that are only 10-15m
  apart.
• It acts over a very short range
• It is not felt by nucleons when they are more
  than 10-15m apart.
• It is selective
• It is felt by neutrons protons, but not by
  electrons

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Nuclei cant be too large
A proton feels electrical repulsion from every
proton in the nucleus
It feels a Strong Nuclear attraction only to
nearby nucleons











In larger nuclei, the electrical force is bigger
while the nuclear force stays the same.










Eventually, the electrical repulsion overwhelms
the nuclear attraction



There are no stable nuclei above Z82 (Lead)
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Discovery of radioactivity
14
Different types of radiation
charged
Marie Curie
a

• --

neutral
g

- charged
b
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a decay
A A-4 4
ZY ? Z-2X 2a
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Conservation of energy in a-decay
Energy of parent
Energy of daughters
parent
daughters
A A-4 4
ZY ? Z-2X 2a
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Conserv. of energy in a-decay
MXc2 Mac2 KE
KE MYc2 - MXc2 - Mac2
MYc2
parent
daughters
v
A A-4 4
ZY ? Z-2X 2a
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Energy balance
daughters
the mass difference, times c2, becomes KE
parent
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KE Mparentc2 (Mdaughters c2)
Some mass is changed into Kinetic Energy
All the a particles have the same Kinetic Energy
a-particle Kinetic Energy
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Beta (b) decay
6C
7N
14
14





? e-


7p 7n
6p 8n






n ? p e-
A A
ZY ? Z1X e-
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Other beta decays
228 228
88Ra ? 89Ac e-
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Tritium Beta decay
3H
3He
e-



3 3
1H ? 2He e-
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Energy balance in beta decay
14Ne-
160 keV
14C
1 keV 1000 eV
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Electron energy in 14C beta decay
None of the electrons have 160 keV of kinetic
energy they all have less than that amount
KEe-
What has happened to the missing energy??
KEe-
160 keV
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Paulis desperate solution
Another unseen particle is emitted in b decay
process
neutrino!!
no charge no mass
n
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14C b decay revisited
6C
7N
14
14
e-
n
14 14
6C ? 7N e- n
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3H b decay revisited
3H
3He
e-
n
3 3
1H ? 2He e- n
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Energy balance in beta decay
daughters
KEe- KEn
parent
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Cosmic gall
NEUTRINOS, they are very small. They have no
charge and have no mass And do not interact at
all. The earth is just a silly ball To them,
through which they simply pass, Like dustmaids
down a drafty hall Or photons through a sheet of
glass. They snub the most exquisite gas, Ignore
the most substantial wall, Cold shoulder steel
and sounding brass, Insult the stallion in his
stall, And scorning barriers of class,
Infiltrate you and me! Like tall and painless
guillotines, they fall Down through our heads
into the grass. At night, they enter at Nepal
and pierce the lover and his lass From
underneath the bed-you call It wonderful I call
it crass.
John Updike
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Radioactive half-life
Initial number of atoms
number of halflives
N N0 ( ½ )n
Number of remaining atoms
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Some half-lives
T1/2

• 3H (?3He e- n) 12.3 yrs
• 14C(?14N e- n) 5730 yrs
• 238U(?234Th a) 4.5x109 yrs
• 235U(?231Th a) 7.1x108 yrs
• 226Ra(?222Rn a) 1600 yrs
• 28Mg(?28Al e- n) 21 hrs
• 213Po(?209Pb a) 4x10-6 s

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Carbon-14 dating
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14C content
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Shroud of Turin