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Author Topic:   Spontaneous fission, decay rates, and critical mass
DWIII
Member (Idle past 414 days)
Posts: 72
From: United States
Joined: 06-30-2011


Message 1 of 29 (647147)
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

Replies to this message:
 Message 3 by RAZD, posted 01-08-2012 8:48 AM DWIII has acknowledged this reply
 Message 4 by NoNukes, posted 01-08-2012 1:09 PM DWIII has responded

  
DWIII
Member (Idle past 414 days)
Posts: 72
From: United States
Joined: 06-30-2011


Message 7 of 29 (647214)
01-08-2012 4:51 PM
Reply to: Message 4 by NoNukes
01-08-2012 1:09 PM


Re: That's just about right...
NoNukes writes:


I have a nit to pick with one statement in the OP.

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.

I don't think the statements have the implication stated above. I am willing to accept that lowering the barrier for decay will have an affect on the spontaneous fission rate. But accepting that hypothesis does not imply a correlation between decay rates and critical mass.

And yet Zen Deist was apparently arguing for lower critical masses on the basis of lower nuclear stability by causing more induced fission events due to more spontaneous fission events, something which both you and I disagree with. Anyway, he seems to have since changed gears somewhat, claiming that enrichment due to lower nuclear stability would also play a factor. Well, we will see, I hope...


I'd also question the relevance of your plutonium evidence. A Pu 238 nucleus behaves very differently in nuclear reactions from a Pu 239 nucleus. Comparing isotopes may not be a good indicator of what would happen if the binding energy for a particular nucleus were to be supernaturally reduced.

I agree that it's not a particularly great example, given that the numbers are all over the board just for those five closely-similar isotopes. You are quite right in that a difference of just one neutron can have profound consequences for many aspects of nuclear behavior; but in the absence of magically increasing overall nuclear decay rates (or equivalently having a complete theory of nuclear stability), perhaps it could be seen as the next best thing for the sake of testing for any such correlations with respect to critical mass.


DWIII

This message is a reply to:
 Message 4 by NoNukes, posted 01-08-2012 1:09 PM NoNukes has acknowledged this reply

  
DWIII
Member (Idle past 414 days)
Posts: 72
From: United States
Joined: 06-30-2011


(1)
Message 13 of 29 (647339)
01-09-2012 10:28 AM
Reply to: Message 10 by RAZD
01-08-2012 9:12 PM


Re: Decay rates, change, and atomic stability
Zen Deist writes:


No one disputes that the spontaneous fission rate would increase.

So it appears that we are all in agreement, as I said in Message 3:

quote:
We are in agreement then, that keeping things working according to the scientific principles, increasing the decay rate results in less stable atomic materials, and that any claim otherwise invokes PFM ...

Well, that goes without saying; it's practically a tautology. A decay rate is (by definition) inversely proportional to stability.


Would you not also agree that this change in stability necessarily affects the behavior of other particles, nuclei, etc, operating under the same laws and forces that regulate decay rates? That this is why the occurrence of spontaneous fission would increase, not just decay events, yes?

There should be no special pleading for one set of particle\behavior compared to others operating by the same laws and forces.

You may be right, but how could we directly test that? Given that (1) spontaneous fission decay events tend to be an extremely small proportion of all decay events for a typical isotope in question, and (2) even among the slightly different isotopes which I put forth as a test sampling, the range of variation of the absolute rate of spontaneous fissions varies by a whopping 6 orders of magnitude, even though the overall decay rates vary by no more than 4 orders of magnitude, the available evidence seems to be inconclusive at best. In fact, the half-lives and the absolute rates of spontaneous fission exhibit less correlation than any of the other four pairings of data which I alluded to earlier.

For all we know, the spontaneous fission decay rates themselves may be extremely sensitive to changes in nuclear stability, and not always in the same direction.


But even a 1% increase would cause more induced fission than now would it not? This would translate to less critical mass needed to achieve a sustained chain reaction would it not?

To initially achieve a chain reaction, perhaps. If the spontaneous fission rate was absolutely zero, it would never get started in the first place (barring an external source of thermal neutrons). But to sustain a chain reaction is another thing entirely, and that's what k=1 criticality (as opposed to k<1 subcriticality) is all about.

If a k=1 chain reaction has already started, you could subsequently PFM-supress all forms of spontaneous decay, including the already-comparatively-rare spontaneous fission events while leaving the specifics of induced fission unchanged, and the chain reaction process itself would be (to an accuracy of many decimal places) completely unaffected.


I am aware of no good reason why the products from fission would necessarily include more neutrons simply because the binding energy changes.

Are they not operating under the same laws and forces that hold the decay particles in the nucleus until decay occurs? Can I affect one without affecting the other(s)? Is there any good reason to think that they would NOT be affected?

Again, for all we know, the specifics of neutron emission rates via fission (such as average number of neutrons released, and/or the energy spectrum of those neutrons, not even to mention rates of subsequent neutron absorption and/or rates of subsequent induced fissioning) may very well be extremely sensitive to small changes in overall nuclear stability, and not always in the same directions.

Edited by DWIII, : re: insufficient evidence

Edited by DWIII, : fixed html-character bug


DWIII

This message is a reply to:
 Message 10 by RAZD, posted 01-08-2012 9:12 PM RAZD has acknowledged this reply

Replies to this message:
 Message 14 by NoNukes, posted 01-09-2012 11:21 AM DWIII has acknowledged this reply

  
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