Suggested+Solutions+to+Fission+and+Nuclear+Reactors

  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.
 * 1: **
 * Nuclide pairs || Q-value for neutron capture (MeV) || Change in E b /A (MeV) ||
 * 235 U/ 236 U || 6.58 || -0.007 ||
 * 238 U/ 239 U || 4.64 || -0.015 ||
 * 239 Pu/ 240 Pu || 6.53 || -0.007 ||

The nuclide pair 238 U/ 239 U have a significantly lower Q-value and a significantly bigger fall in E b /A than the other pairs. This can be explained by the pair-pair configuration in the 238 U 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 σ f ).

2:

> 99 Y: M( 99 Y)-M( 99 Ru)=17.4 MeV > 139 Cs: M( 139 Cs)-M( 139 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">La)=6.5 MeV
 * 1) 239 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Pu+ n → 99 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Y + 2n + 139 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Cs
 * 2) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Q-value: 191.42MeV
 * 3) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The energy which is released by disintegration after stability is
 * 1) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">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.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> **3:**


 * 1) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">1.0 g 239 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Pu = 2.5•<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">10  21 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> atoms. Number of fissions per seconds is σ •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">ϕ •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">N  t <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> = 1.89 •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">10  14 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">, which will give an effect of 3.6 •10 16 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">MeV (5811W)
 * 2) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The formation of 240 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Pu: σ•<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">ϕ •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">N  t <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">= 6.8 •10 13 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">s -1 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">. After 100 days of irradiation 0.232 g Pu will be made.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">4: **


 * 1) 232 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Th+ n→ 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Th → 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Pa → 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U
 * 2) 133 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">I.
 * 3) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">One ton 232 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Th equals to 2.6 •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">10  27 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> atoms. The rate of formation for neutron capture ( 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Th): σ •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">ϕ •Nt = 7.37•10 24 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">cm 2 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">•10 14 <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">n <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> cm -2 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">s -1 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">•<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">2.6 •<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">10  27 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">atomer= 1.91 •10 18 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">atoms s -1
 * 4) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">It will take 37 hours of irradiation to form enough 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Th to give 100 g 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U, but disintegration of 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Pa to 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U must be waited.
 * 5) <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">100 g 233 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;"><span style="font-family: 'Times New Roman','serif'; font-size: 16px;">U: D=λN = 3.56 •10 10 <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Bq (35.6 Gbq)

Exercises with Fission and Nuclear Reactors

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