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Author Topic:   Spontaneous fission, decay rates, and critical mass
DWIII
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Message 1 of 2 (647103)
01-08-2012 6:28 AM


In "How did the Aborigines get to Australia?" (Message 57):

Zen Deist writes:


Fission is a type of decay process.

http://en.wikipedia.org/wiki/Spontaneous_fission

quote:
Spontaneous fission (SF) is a form of radioactive decay characteristic of very heavy isotopes. Because the nuclear binding energy reaches a maximum at a nuclear mass greater than about 60 atomic mass units (u), spontaneous breakdown into smaller nuclei and single particles becomes possible at heavier masses. ...

As the name suggests, spontaneous fission gives much the same result as induced nuclear fission. However, like other forms of radioactive decay, it occurs due to quantum tunneling, without the atom having been struck by a neutron or other particle as in induced nuclear fission.

Spontaneous fissions release neutrons as all fissions do, so if a critical mass is present, a spontaneous fission can initiate a self-sustaining chain reaction. ...


The process that results in alpha and beta decay is the same process for spontaneous breakdown into nuclei larger than a Helium nuclei (alpha particle).

You can't affect decay rates without affecting fission decay.

When you reduce the nuclear binding energy or lower the barrier for radioactive decay to occur, and reduce the decay rate, you would increase the occurrence of all forms of radioactive decay, including fission.

This means that the critical mass required to reach a sustained reaction is reduced.

Nonukes quite correctly points out the errors in the preceding, namely, that the phenomenon of induced fission, which proceeds extremely rapidly on the successful absorption of a free neutron, is very different from spontaneous fission, which is an extremely rare phenomenon compared to the typical natural decay rate of a radioactive substance.

The statements "You can't affect decay rates without affecting fission decay" and "When you reduce the nuclear binding energy or lower the barrier for radioactive decay to occur, and reduce the decay rate, you would increase the occurrence of all forms of radioactive decay, including fission" and "the critical mass required to reach a sustained reaction is reduced" collectively imply some sort of correlation between decay rates and critical mass. This is arguably not the case. Here is the raw data for fissionable isotopes of plutonium, extracted from Wikipedia (Critical mass and Isotopes of plutonium)


Isotope Critical mass Half-life Proportion of
(bare unbounded sphere) spontaneous fission events
-----------------------------------------------------------------------------
Pu 238 9 kg 87.7 y 1.9 * 10^ -7 %
Pu 239 10 kg 24100 y 3.1 * 10^-10 %
Pu 240 40 kg 6560 y 5.7 * 10^ -6 %
Pu 241 12 kg 14.3 y 2.4 * 10^-14 %
Pu 242 85 kg 375000 y 5.5 * 10^ -4 %
-----------------------------------------------------------------------------

Dividing the proportion of spontaneous fission events by the half-life (where half-life is inversely proportional to activity) would, in addition, give an indication of how many spontaneous fission events are to be expected per unit time per unit mass.

It turns out that, as far as I can see (at least for plutonium), there seems to be essentially no correlation between the following paired sets of data:

1) half-life and proportional spontaneous fission rate
2) half-life and critical mass
3) proportional spontaneous fission rate and critical mass
4) absolute rate of spontaneous fission and critical mass

(Feel free to make your own scatter-plots, of course.)

As Nonukes points out, the rate of spontaneous fission events has nothing to do with the size of a fissionable isotope's critical mass (all you really need is one fortuitous event in a critical mass to start a chain reaction), and even less to do with the overall decay rate of a fissionable isotope that is not undergoing a chain reaction.

An analogy would be what is known as the "percolation threshold" for feedback systems, such as a forest fire, or a field of upright dominoes. It's a given that the probability of a tree spontaneously catching fire is extremely low, but, if that probability isn't precisely zero, a spreading conflagration would be inevitable solely dependent on tree flammability, asymptotic density, and size of the forest.


DWIII

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Message 2 of 2 (647148)
01-08-2012 8:05 AM


Thread Copied to Dates and Dating Forum
Thread copied to the Spontaneous fission, decay rates, and critical mass thread in the Dates and Dating forum, this copy of the thread has been closed.

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