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Decay rate help

  1. Sep 27, 2010 #1
    Decay rate help
    I've been debating decay rates with another poster in another forum. Basically, the other poster has stated

    "The half-life/decay rate of the substances used in nuclear power generation have nothing to do with the generation of power. That they ARE radioactive is. Spent fuel has very little to do with the ratio of remaining parent atoms to inert daughter or non-inert daughter atoms. It has to do with neutron saturation in the reactor. The point that you keep missing is can be explained this way: If you started off with 100% U235 (half-life = 700,000,000+/- years), you would wind up with "spent" fuel rod packs with more than 95% of the U235 still present. It certainly doesn't seem like - with more than 95% fissionable material left - the half-life/decay rate has much to do with the fuel rod packs becoming spent. But you keep thinking it does."

    I've been trying unsuccessfully to locate something that says that decay rates must be considered during design and operation of a nuclear plant.

    Can anyone help me with an on-line, reputable source?

  2. jcsd
  3. Sep 27, 2010 #2


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    Decay rates of U-235, U-238, or the fission products?

    In an LWR, the enrichments are on the order of 3.2 - 4.95% depending on the type of reactor, fuel design, batch size and cycle length. The decay rates of U-235 and U-238 are essentially irrelevant. The U-235 fissions, with some in U-238, and some U-235 doesn't fission but become U-236, which decays or absorbs a neutron to become U-237. Some u-238 absorbs a neutron and becomres U-239, which decays to Np-239, which decays to Pu-239. Np-239 absorbs a neutron and becomes Np-240, which decays to Pu-240. Pu-239 may fission or absorb a neutron and become Pu-240, which could fission or become Pu-241. Further neutron absorption and decay can produce isotopes of Am and Cm, which accumulate at high burnups > 30-40 GWd/tU (~3-4% fima).

    Decay rates of short-lived and medium-lived fission products are important depending on their cross-section, and the decay rates of delayed-neutron precusors are critical to control.

    The decay rates of Te-135/I-135/Xe-135 are important in assessing the impacts of Xe kinetics during rapid power maneuvers.

    The higher the decay rate (and shorter the half-life), the quicker a given nuclide reaches saturation during operation, although it also decays to more a stable nuclide, which accumulates unless it has a high cross-section. Nuclides with half-lives on the order of days would reach equilibrium/saturation in weeks. As long as power is constant, the concentration of isotopes accumulates according to their fission yields, decay rates of their precursors and their own decay rates.

    Most of the physics of transmutation and decay is embedded in lattice cross-section and core depletion/simulation codes. Otherwise, the physics is discussed in textbooks on nuclear reactor physics.

    See - http://www.sprawls.org/ppmi2/RADIOACT/
  4. Sep 27, 2010 #3
    Thanks, astronuc. I'll look at the information.
  5. Sep 27, 2010 #4
    It's not an online source, but Todreas and Kazimi's introductory text on thermal hydraulics has many examples and problems where the decay heat of the fission products is 8-10% of maximum thermal power. Since this power is from decay, it cannot be immediately shut down like the fission process. In this sense, you have to design the reactor system to accommodate this if you need to scram when pumping power is lost.

    I'm guessing that was your original thought?
  6. Sep 27, 2010 #5

    I was originally thinking that decay rates needed to be considered because you have to know how much fuel mass needed to be included just to produce the desired amount of heat for power generation. As I've learned more (I know enough physics to be dangerous, but next to nothing about reactors) I've learned more about the decay chains and daughter products etc. It just seems logical to me that you can't ignore a fundamental property of the fuel - its half life - in the design and operation of a nuclear plant. But I'm having trouble finding anything that specifically states that.

    Thanks for the information.
  7. Sep 28, 2010 #6


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    If one is concerned about the decay of the fuel, really the U-235. Then one can simply do the calculation with the half life, 700,000,000 years. Ref: http://www.nndc.bnl.gov/chart/reCenter.jsp?z=92&n=143 (select zoom 1)

    Determine the decay constant - λ = 0.693/t1/2, where time, t is in seconds.

    The calculate how much fuel decays in 10 years.

    Current reactors operate with 18 to 24 month cycles (1.5 to 2 years), and the fuel is resident for 2 or 3 cycles, and in rare cases 4 cycles. Some European plants still operate with annual cycles, so some fuel might be resident for 6 or 7 cycles, even 8. But resident time is no more than 8 years.

    Decay of the fuel, U-235 and U-238, is not a concern for a reactor, not even for one fueled by Pu-239, which has a half life of 24400 years. Ref: http://www.nndc.bnl.gov/chart/reCenter.jsp?z=94&n=145 (Zoom 1)
  8. Sep 28, 2010 #7


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    Commercial nuclear power uses the controlled fission of uranium atoms to produce heat, it does not depend on the natural decay rate of the fuel at all.

    A thermoelectric isotope generator, such as those used by deep space satellites for power source, do make use of natural radioactive decay to generate electricity, although by a completely different method.
  9. Sep 28, 2010 #8

    But doesn't the "controlled fission reaction" in fact depend upon decay rates? Don't you have to provide enough fuel to keep the reaction supercritical, while controlling the criticality to prevent a meltdown? You don't just glom together a mass or radioactive materials do you? Calculations are made to determine what mass of fuel in what concentrations are necessary to produce a controlled chain reaction, and all of that ultimately depends upon decay rates?

    I understand that once the reaction is started it is all about controlling it since there is enough fuel present in sufficient quantities to keep it going. But how do you set all of this up without consideration of decay rates? How do you know how much fuel is needed, the kind of fuel, the reactor configuration, the safety systems, etc., without considering decay rates? How do plant operators maintain control without taking into account decay rates of daughter isotopes and their rates of production? How are safety systems designed without taking into consideration decay rates?
  10. Sep 28, 2010 #9


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    No, the fission of a nucleus by the absorption of a neutron is a completely different and independent process from natural radioactive decay.

    Natural radioactive decay is when an unstable nucleus spontaneously disintegrates, transforming into a different nucleus and releasing energy. The probability of this process occurring is dependent on the properties of the isotope.

    Neutron fission is when a neutron is absorbed by a nucleus, briefly transforming it into a new, highly unstable isotope, which nearly instantly decays by fission.

    There is no way to change the rate of natural radioactive decay. However, a fission chain reaction can be controlled by changing the probability the neutrons will be absorbed by the fuel to cause more fissions. The is accomplished by adding neutron-absorbing materials to the reactor (e.g. control rods, soluble boron), or by changing the properties of the neutron moderator (e.g. water temperature/boiling rate).
    Last edited: Sep 28, 2010
  11. Sep 28, 2010 #10
    To make a fission reactor, you do basically, 'glom' together a bunch of fissile (meaning a neutron can fission it) material. Eventually you get enough of it together, that there is enough of it to keep a chain reaction going.

    Fresh fuel in a nuclear reactor is slightly radioactive. That is the uranium in the fuel does decay with the passage of time. However, when you run the numbers, the fuel decays VERY slowly, such that in the lifetime of a person, the composition of the fuel has not significantly changed due to the radioactive decay. It would take 700 million years to loose half of it, so 100 years results in very little change.

    The chain-reaction has very little to do with the natural radioactive day. Uranium is instead induced to fission (splitting into 2 atoms) when hit with a neutron. This reaction also produces a number of neutrons. Some of these neutrons go on to cause other uranium atoms to fission (continuing the chain) while others are lost to other effects. Controlling a reactor involves balancing the production of neutrons with the loss of neutrons to keep the power stable.

    Radioactivity of spent fuel comes from more than one source. First, as expected, there is radioactivity of the uranium still in the fuel. Next there is radioactivity due to the daughter atoms (the result of splitting). These atoms are unstable and decay (giving off heat) until they reach a stable isotope. Finally there are the activated atoms. Some atoms when in the reactor will capture one of the free neutrons that hit. These eventually turn into things like neptunium, plutonium, americium and others. These are also radioactive.

    Radiation form the first source has actually decreased because you now have less uranium present then when you started. The second source produces the most radioactivity, these are the ones that tend to decay quickly (know as fission products). These are the ones that produce most of the heat after it is out of the reactors and require the that fuel remain in cooling ponds. The last group has longer half-lives then the second group. This means they are less radioactive, but also last longer.

    Yes, when in the reactor, the energy released by these decays contribute to the power of the reactor. However they are not the main source. They influence the design by requiring that the fuel continue to be cooled even after shutdown.

    Hopefully this helps.
  12. Sep 28, 2010 #11
    Thanks. That does help. Just one more question (I think).

    Where do the initial neutrons come from that starts the chain reaction? If it is the natural decay of the fuel, don't you need to have a "sufficient" number of neutrons to start the chain reaction? or will one do the trick? If there is a minimum number needed, isn't that fuel, fuel density, and decay rate dependent?
  13. Sep 28, 2010 #12
    Yes, you need a source of seed neutrons, but you don't need very many. Once you have seed neutrons the number of neutrons produced by the chain reaction very quickly swamps the seed source. There is no real need for a specific number of neutrons to start. Theoretically, 1 could do it, however, the one neutron could also be lost to another process. Practically, any neutron sources produce more then enough to start up a reactor.

    I don't actually know if they include a neutron source in power reactors for this reason. (I know that for nuclear weapons, they include a neutron source, but I think that that is just speed up the process). I think for a reactor there maybe enough stray neutrons floating around from spontaneous decay and cosmic radiation but I'm not sure if the speed it along. For start ups after shutdowns, you might be able to rely on delayed neutrons, but I also don't know about that.

    Even if you did have a neutron seed source for a reactor, that activity represents a negligible contribution to the on power neutron flux. It would only matter when the reactor is at very low powers.
  14. Sep 28, 2010 #13


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    The initial neutrons can come from radioactive fission products in used-fuel which emit neutrons. The number of neutrons generated from used fuel is dependent on its burnup (how long the fuel has been used in the reactor). The longer fuel is used in the reactor, the more fission products that produce spontaneous neutrons will be built up.

    Alternatively, you can use an external neutron source. These use Americium and Beryllium to produce an [tex](\alpha,n)[/tex] reaction. The amount of neutrons produced from these merely depends on the mass of Am and Be you have.

    The minimum number of neutrons needed to start a chain reaction is 1, although if the reactor is only critical then each generation would only produce on average 1 neutron, and odds are pretty soon you'd be left with none :smile:

    Note that a reactor can be critical with zero neutrons. Criticality is a measure of how fast neutrons multiply, not how many you have or what the power level is.
  15. Sep 28, 2010 #14
    Thank all of you. You've been very helpful. Looks like I need to do a mea culpa on the other board.
  16. Oct 18, 2010 #15
    The decay rates of the initial fuel load, typically U235 and sometimes Pu239 are really not part of reactor design. Some of the U239 is converted by neutrons into Pu239 during operation, but this decay rate also doesn't really matter. The fact that they are slightly radioactive can be used to 'seed' the initial neutrons upon startup, but this is a minor consideration. However, the only reason our current fission based reactors work at all is due to delayed neutrons from the fission daughter products. They allow the reactor to work in the 'critical' realm (neutron flux = constant value), and give us control of said neutron flux with the control rods. In reality, the prompt neutrons (from the fuel) are adjusted so they fall slightly below the 'critical' realm, and the delayed neutrons (seconds to minutes later due to the daughter products half-lives) add to this so that the reactor is usually operating at criticality (steady state power). Without this slower feedback mechanism, the reactor would be nearly impossible to control.
  17. Oct 18, 2010 #16
    Meant: Some of the U238 is converted by neutrons into Pu239 during operation
  18. Oct 19, 2010 #17
    The decay chain and decay rate of fission product xenon-135 is very important in the start-up of reactors. It has a thermal neutron absorption cross section of ~2,000,000 barns, and is rightly called a reactor "poison". See


    The Chernobyl reactor accident is blamed in part on the concentration of the radioactive isotope xenon-135.

    Bob S
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