It is noteworthy to notice the Q-value for the neutron capture and the change in binding energy per nucleon for each of the isotope pairs.
Nuclide pairs
Q-value for neutron capture (MeV)
Change in Eb/A (MeV)

The nuclide pair 238U/239U have a significantly lower Q-value and a significantly bigger fall in Eb/A than the other pairs. This can be explained by the pair-pair configuration in the 238U nucleus, which makes it less favorable to bind another neutron. On the other hand, for pair-odd nuclei it is much more favorable to bind another neutron to achieve a pair-pair configuration. This is shown from the cross sections for interaction with thermal neutrons (σ and σf).


  1. 239Pu+ n →99Y + 2n + 139Cs
  2. Q-value: 191.42MeV
  3. The energy which is released by disintegration after stability is
    99Y: M(99Y)-M(99Ru)=17.4 MeV
    139Cs: M(139Cs)-M(139La)=6.5 MeV
  4. 2/3 of this energy will disappear with neutrinos. Some of the disintegrations have too long half-lives to have an effect on the reactor safety.


  1. 1.0 g 239Pu = 2.5•1021 atoms. Number of fissions per seconds is σϕNt = 1.891014, which will give an effect of 3.6•1016 MeV (5811W)
  2. The formation of 240Pu: σ•ϕNt= 6.8•1013s-1. After 100 days of irradiation 0.232 g Pu will be made.


  1. 232Th+ n→233Th233Pa233U
  2. 133I.
  3. One ton 232Th equals to 2.61027 atoms. The rate of formation for neutron capture (233Th): σϕ•Nt = 7.37•1024cm2•1014n cm-2s-12.61027atomer= 1.91•1018atoms s-1
  4. It will take 37 hours of irradiation to form enough 233Th to give 100 g 233U, but disintegration of 233Pa to 233U must be waited.
  5. 100 g 233U: D=λN = 3.56•1010 Bq (35.6 Gbq)

Exercises with Fission and Nuclear Reactors