When do fission products get cooler than fuel?

[snorkack]

Main nuclear fuel is U-235.
Actinium series to stable Pb-207 includes 7 alpha and 4 beta decays. Total energy yield 46,4 MeV.
In the main branch, the 4 beta decays carry around 3 MeV energy. Meaning the alpha decays are about 43 MeV... and they have high biologic effectiveness, around 20. Meaning U-235 does about 860 MeV worth of damage in its 710 million year half-life... about 1200 keV per million years.
When U-235 is fissioned, some daughters are stable. Others are hot but short-lived and promptly decay to stable daughters in 100 years or less half-life
This leaves 7 or so long lived fission products. But even these are beta active... limited total energy, limited biologic effectiveness and limited yield.

Are long lived fission products actually hotter than the original unburned U-235+daughter chain?

 

[Drakkith]

What do you mean by 'hotter' and 'cooler'? Are you referring to their literal temperature?

 

[snorkack]

What do you mean by 'hotter' and 'cooler'? Are you referring to their literal temperature?

No, as can be seen from my arguments.
"Hotter" as in "more biologically damaging radiation per unit time".

 

[Astronuc]

One could use a spreadsheet and look at the individual and sum of activity (decays/time) and energy deposition (activity * energy/decay) for the longest living fission products, and perhaps the medium fission products, and compare to the activity and energy deposition of ²³⁵U. Furthermore, one may consider the specific activity, e.g., per gram of material.

https://en.wikipedia.org/wiki/Long-lived_fission_product#The_7_long-lived_fission_products

However, consider that while ²³⁵U is the principal fuel, some fission occurs in ²³⁸U from fast neutrons, and perhaps more importantly, both nuclides are transmuted by neutron capture to transuranic radioisotopes, ²³⁶Np and ²³⁹Pu, respectively, which can also transmute to ²³⁷Np and ²⁴⁰Pu, respectively, and so on.

See also, the plot of activities of FP and TU radionuclides:
https://www.titech.ac.jp/english/news/2017/039701

On a related subject matter

Transmutation of long-lived fission products in an advanced nuclear energy system​

https://www.nature.com/articles/s41598-022-06344-y

 

[snorkack]

Looks like the long lived fission products, dominated by Tc-99, are 1000 times cooler than uranium, and fission products dominated by Sr-90 get cooler than uranium in 300 years or so... except for the transuranium elements, due to which the radioactivity lasts closer to 10 000 years.

 

[rpp]

If you are looking for a general answer of when spent fuel is less radiotoxic than natural uranium ore, there are several plots that you can find on the internet.

For example, this plot shows it will occur in about 200,000 years.
https://en.wikipedia.org/wiki/File:Spent_nuclear_fuel_decay_sievert.jpg

There are other plots you can see by doing a search on "image radioactive decay radiotoxicity"

 

[Melbourne Guy]

No, as can be seen from my arguments.
"Hotter" as in "more biologically damaging radiation per unit time".

FYI, I couldn't "see" that from your OP, @snorkack, but are you able to share the context for your question? Radiation toxicity depends on many factors such that a 'cooler' element may be more lethal than a 'hotter' one through the circumstances of contact.