Lecture 22' Spontaneous Nuclear Transformations Radioactive Decay

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Lecture 22. Spontaneous Nuclear Transformations
(Radioactive Decay)
If iron is the most energetically favorable
configuration of nucleons, why are there
other-than-iron nuclei in the Universe?
Binding energy per nucleon (EB/A), MeV
Mass number, A
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Lecture 22. Spontaneous Nuclear Transformations
(Radioactive Decay)
Several types of processes that result in an
increase of the binding energy per nucleon (and,
thus, in the reduction of the total energy

• Spontaneous nuclear transformations (radioactive
  decays) the processes that transform less stable
  nuclei into more stable ones.
• - ? decay
• - ? decay (A is fixed)
• - ? decay
• - spontaneous fission (Agt232)

• Induced nuclear transformations (nuclear
  reactions) processes that also result in
  releasing some (bind) energy, but which, in
  contrast to the spontaneous nuclear
  transformations, require some activation (high
  temperatures, bombardment by neutrons, etc.)
• - nuclear fission
• - nuclear fusion

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Nuclear Fusion and Fission
The process through which a large nucleus is
split into smaller nuclei is called
fission. Fusion is a reverse process.
Fission and fusion are a form of elemental
transmutation because the resulting fragments are
not the same element as the original nuclei.
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?, ?, ? decays

• A nucleus is unstable if a physical process
  exists that enables its nucleons to settle in a
  state with a lower rest energy. Such a nucleus
  will spontaneously (sooner or later) decay to a
  lower-energy state.
• Lower energy states exist if
• it doesnt have the optimal mix of protons and
  neutrons. Any weak-interaction processes that
  optimize the ratio of neutrons to protons without
  changing the total number of nucleons in a
  nucleus (Aconst) are called Beta-decay
  processes.
• there is an optimal (for a given A) mix of
  protons and neutrons, but A is so large that it
  is energetically favorable for the nucleus to
  fragment into smaller pieces by emitting
  (Alpha-decay, AfAi-4).
• A nucleus has a nucleon that for some reason is
  in an excited state (Gamma decay, emisson of
  ?-photons).

?-decay
?-decay
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?, ?, ? decays (contd)
1896 Becquerel discovers radioactivity
The Nobel Prize in Physics 1903
? 3 types observed ?, ? and ?
A. H. Becquerel
Pierre Curie
Marie Curie
?
?
?
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? decay ( N/Z ratio is not optimal )

• neutron decay (?-, lowers the N/Z ratio)
• proton decay (?, raises the N/Z ratio)
• electron capture (raises the N/Z ratio)

The three most common ? decay processes
For these processes to happen spontaneously, the
energy ?E released by the process must be
positive.
Aconst
For example, ?- decay occurs if
(the rest mass of both neutrino and anti-neutrino
is negligibly small)
In terms of atomic masses (add Zme to both sides
of equations)

• ?- decay
• ? decay
• el. capture

A nucleus will only be stable against ? decay if
its atomic mass is smaller than that of the two
nuclei with the same A and adjacent values of Z.
Q The atomic mass of 1530P is 29.978u, while the
atomic mass of 1430Si is 29.974u. Which decays to
which, and by what process?
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? decay and Discovery of Neutrino
It is very difficult to detect neutrinos and
anti-neutrinos generated in the beta decay
processes (in contrast to electrons). Neutrinos
very weakly interact with matter they are
uncharged, move with v c and interact with
other particles only via weak interaction. The
mean free path of neutrinos in regular matter is
100 light-years (!) Flux of solar neutrinos
5?106 cm-2s-1. Solar neutrinos shine down on us
during the day, and shine up on us during the
night.
Nobel 1938
Physicists were puzzled by an apparent violation
of the energy and momentum conservation in beta
decay. Pauli (1930) proposed that an undetected
particle participates in beta decays. Fermi
(1933) called the particle neutrino and
contributed to the theory of beta decay. The
first detection by Fred Reines and Clyde Cowan
in 1956.
Energy spectrum of electrons from the beta decay
Super-Kamiokande neutrino detector
Nobel 1995
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? decay

• Alpha decay very massive nuclei shed alpha
  particles (24He nuclei) to decrease electrostatic
  repulsion.
• Why not shed other kinds of particles?
• binding energies for other low-mass
  possibilities are too small (strong pairing
  effect in even-even 24He)
• ejection of higher-mass nuclei are
  statistically unlikely.

Conservation of energy
Alpha decay occur spontaneously only if the
initial atomic mass is greater than the final
atomic mass plus that of helium.
Example
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? decay (contd)
Analysis of the binding energy equation in the
liquid-drop model shows that ? decay becomes
energetically possible for A ?146. Within the
range 146 A 209 stable and unstable nuclei
with nearly optimal N/Z coexist, all nuclei with
Agt209 are unstable those with optimal N/Z
undergo ? decay.
Binding energy per nucleon (EB/A), MeV
Mass number, A
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Tunnel theory of ? decay
The question however remains how an ? particle
can escape ?
Indeed, if we assume that the ? particle
pre-exist within a heavy nucleus, its a
subject of the following potential
The height of the potential barrier can be
estimated as follows
However, decay ? particles have energies within
the range 4-9MeV!
Gamow and, independently, Gurney and Condon,
developed the theory of ? decay based on
quantum-mechanical tunneling (1928).
Attempt rate
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Tunnel theory of ? decay (contd)
Tunneling probability
Decay time
Makes sense! Also, the decay time depends on the
energy of ? particles as expected
The slowest decay 90232Th - ?1010y. The
fastest decay 84212Po - ?3?10-7s.
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Decay Rates
Common feature of spontaneous decays fixed
probability of occurring in a given time
interval. If an unstable nucleus has a 50
probability of decaying within the first second,
it will have the same 50 probability of
surviving the next second, and so on.
Decay constant
If we have a sample containing N unstable nuclei,
the number of decays in unit time would be
the samples activity
activity also exponentially decreases with time
The unit of activity, the Becquerel
Half-life (the time that it takes to cut in half
the number of unstable nuclei)
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Problem
A sample contains 4.5g of 13H (tritium), which
decays by a ?- decay to 23He with a half-life of
12.26 yr. (a) what is the activity of the sample?
(b) About how long would it take the number of
tritium atoms to decrease by a factor of a
million?
First, we need to find N. The Avogadro number of
tritium atoms (the number of atoms in 1 mole)
have a mass of 3g.
Avogadros number
NA ? 6.022045?1023
Decay constant
Activity of the sample