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USING RADIOACTIVE DECAY SERIES TO INVESTIGATE SEA FLOOR
SPREADING.
Chapter 18
Posted on Capt 23rd September 2005
If the daughter and granddaughter etc of a radioactive nuclide are also
radioactive, then a radioactive series is set up until eventually a stable nuclide
results. There are several such radioactive series (see eg Chapter 18 display
material 80 O, and question 140 D).
Each nuclide in the series will have its own unique half life. Given enough time
the intermediate daughter nuclides will establish a steady state decay chain
(“secular equilibrium”) in which all the nuclides will decay at the same rate.
This dynamic equilibrium takes about five half lives of the shorter lived
nuclide. Conversely any disequilibrium between a pair of nuclides in a decay
chain records an event that must have disturbed the equilibrium situation in
some way.
This has been used by geophysicists to measure the flow rate of the magma
that feeds the spreading of the oceanic plates.
Part of the thorium series is used. The ratio of 226-Ra and 210-Pb has been
measured in samples of magma retrieved from 2.5km below the surface of the
ocean.
The half life of 226-Ra is 1600 years, while that of 210-Pb is just 23 years. So
any deviation from equilibrium indicates a disturbance in typically the last 5 x
23 = 115 years or so. As the magma rises the pressure falls and its rate of
melting increases. The two nuclides are incorporated into the melting magma
at different rates, so the speed of the magma has been determined to be a
few metres per year, which is much faster than the sea floor spreading at
typically cms per year.
Ref: Nature 22nd September p485-6.
ACID TEST OF E = MC SQUARED
Chapters 6,7,11,15,16,18
Posted on Capt 30th December 2005
Perhaps the most amazing prediction of Einstein’s Special Theory of Relativity
is E = mc2. If it turned out to be just slightly incorrect, it would have far
reaching consequences.
The latest direct test shows that it is precise to 0.00004% or better than 1 part
in a million. Accurate measurements of atomic mass difference and gamma
ray energies following neutron capture have been carried out. Two separate
neutron capture reactions were studied in silicon-28 and sulphur-32. Both
were of the form AX + n → A+1X + gammas.
The masses were found by ‘cyclotron resonance’. An ion moving at speed v
in a magnetic field B will follow a circular orbit radius r with a circulation (or
cyclotron) frequency fC.
Equating the centripetal force (mv2)/r and qvB, gives m = (rqB)/v Now fC = w/
2, and angular frequency  = v/r, so m = (qB)/(2  fC)
fC is easy to measure, and the ions before and after neutron capture were
kept circulating in the magnetic field for several weeks.
The mass of the original free neutron is already known.
Gamma ray energies after neutron capture were found via the Planck
relationship E = hf, where f was calculated from c = f . The wavelength for
the gamma rays was found by diffraction using the Bragg formula 2 d sin = n
 The crystal lattice spacing d was known, and it is the measurement of the
diffraction angle  that sets the limit to the precision of the experiment. The
gamma energies are typically 5MeV, and the resulting diffraction angle is
about 0.1 degrees.
The result is 55 times more accurate than the previous best direct test using
comparing the electron and positron masses to the gamma ray energies when
they annihilate. Perhaps the very first test of Einstein’s energy mass
relationship was the work of Cockcroft and Walton when they ‘split’ the atom.
Ref: Nature 22/29 December 2005 pp1096-7
ENRICHMENT OF URANIUM - some simple arithmetic
Chapter 18
Posted on Capt 12th January 2006
Natural uranium = 0.7% fissile U-235 and 99.3% U-238
Nuclear power stations require typically 2.5% enrichment [2.5% U-235 and
97.5% U-238]. This is referred to as reactor grade material.
It is an increase by a factor of 2.5/0.7 = 3.6 over natural uranium.
Weapons grade uranium is typically 90% enriched [90% U-235 and 10% U238]
At first sight this appears a large jump from reactor grade material to get
weapons grade material: 90/2.5 is a factor of 36 over the reactor grade value,
or ten times more than the enrichment required for reactor grade material in
the first place from natural uranium. [36/3.6 = 10]
The name enrichment is misleading. What is actually being done is that the
non-fissile U-238 is being preferential removed - so concentration would be a
better name for the process.
Consider 1 tonne natural U. It contains 7kg of fissile U-235. How much U-238
must be removed so that 7kg = 2.5% (reactor grade) of the remaining total?
7/x = 2.5/100
x = 280 kg remains and thus 1000 - 280 = 720kg U-238 has been removed.
ie over 7/10ths is already removed from 1 tonne of natural uranium to get to
reactor grade material.
To get weapons grade material:
7/y = 90/100
y = 7.78kg is all that must remain of the original 1000kg
So you only need to remove another 272.22 kg from the 280kg of reactor
grade material to get weapons grade.
The law of diminishing returns does not set in. Weapons grade material is not
36/3.6 or ten times ‘further away’. By the time you have reactor grade material
you are over 70% of the way to having weapons grade material.
If fact you can make a nuclear bomb with only 40% enrichment.
Ref: Lecture “Nuclear Weapons: the technology of destruction” by R
Marshall.
A NEW WAY TO MAKE ELEMENTS
Chapter 18
Posted on Capt 25th April 2006
Physicists have long thought that supernovae fuse the elements heavier than
iron together. But this does not explain the existence of some of the rarer
nuclei found in our solar system. To produce them, a new process has been
proposed that involves the antineutrinos that supernovae generate in huge
numbers.
In supernovae, most heavy elements arise when helium nuclei assemble into
more massive nuclei, which then absorb neutrons that decay into protons.
These rapid reactions forge elements that climb the periodic table. However,
the sun and meteorites contain some isotopes of the metals molybdenum and
ruthenium with a high proportion of protons, but with no clear origins in the
accepted series of reactions.
Recently astrophysicists have realised that there is a proton-rich region
surrounding the fresh neutron star during the first few seconds of the
supernova explosion. Isotopes that already have a high fraction of protons
cannot capture these additional protons and progress to new elements
because of the repulsive force from the positive charges jammed into their
nuclei. But some of the protons in this region transform into neutrons by
reacting with antineutrinos streaming from the neutron star. These extra
neutrons are critical during the early seconds when the material is still hot
enough to make heavy, proton-rich isotopes. Some nuclei packed with the
maximum allotment of protons grab a neutron and so generate enough
binding force to capture another proton through the strong nuclear attraction.
Within a few seconds, this cycle creates a series of stable isotopes containing
as high a proportion of protons as nuclear forces allow — including the
problematic varieties of molybdenum and ruthenium.
Ref: Physical Review Focus 21st April 2006.