Fission

SCI 270: On Nuclear Technology Practice Problems

9. Nuclear Fission Energy and Reactions

1. Give the nuclear reactions for the syntheses of neptunium and plutonium used in the fast breeder reactor for their productions.

   Nuclear reaction: _________________________________________

   Half lives: ^239Np ______________ ^239Pu ______________

2. Consult a handbook or a nuclear data source and give the range of known (or synthesized) plutonium isotopes. Which one has the longest half life and what is its decay mode?

   Source: _______________________________
   Range of mass numbers of Pu isotopes: From ________ to _________
   Isotope with the longest half life ____________	Decay (modes): _____________________________

3. Assume the thermal-neutron induced fission of ²³⁵U (mass = 235.0439) gives two fragments of mass 140 and 93, and the some neutrons. After having consulted the properties of nuclides of mass numbers 140 and 93, we know that ¹⁴⁰Ce (mass = 139.90539) and ⁹³Nb (mass = 92.90638) are stable nuclides. Write the nuclear reaction equation for this fission process. Estimate the total energy (including energies of beta-decay of the fission products) in this fission process.

   Fission reaction:_________________________________________

   Energy released: _ Q = ___________ MeV/fission Energy released: _ Q = ___________ J/mole

4. How much natural uranium must be processed in order to produce 1.0 kg of ²³⁵U, if only 50% of this isotope is extracted from natural uranium? What methods are used to separate ²³⁵U from natural uranium?

   Abundances of ^235U ___________ %; ^238U ________________ %

   Amount of natural uranium required: _________________ kg

   Methods used for extracting ^235U: Gas diffusion of UF6 based on mass difference. _ ________________________________________________ ________________________________________________ ________________________________________________

The following question are provided to help your study

1. What is a moderator? What are the desirable properties of a compound to make it a good moderator? Why are heavy water and graphite used as moderator for nuclear reactors using natural uranium as fuel, but normal distilled water not a suitable moderator?
2. Assume the abundance of ²³⁵U to be 5.0% when the earth was created. Calculate the age of the earth from the distribution of ²³⁵U and ²³⁸U (now 0.72 % and 99.28 %). Note that the assumption may not be valid.

   This problem may be a challenge to some of you, but hint will be given on the page linked below.

Answers to Practice Problems 9 are available, but do your part first. Your skills are tested and they are yours forever.

Answers

SCI 270: On Nuclear Technology Practice Problems
Answers are given for your reference only. Please do your part of the learning, because no one else will be able to do that for you. Your skills of problem solving are tested and useful in the future. Answers are useless. Acquiring skills and abilities are the goals of learning, marks indications of your performances on these tasks.

1. Give the nuclear reactions for the syntheses of neptunium and plutonium used in the fast breeder reactor for their productions.

   Nuclear reaction: ____^238U + n ® ^239U + g ® Np + b ® Pu + b ____

   Half lives: ^239Np ___ 2.35 d _____ ^239Pu __ 244e4 y __

2. Consult a handbook or a nuclear data source and give the range of known (or synthesized) plutonium isotopes. Which one has the longest half life and what is its decay mode?

   Source: _____________ Varies __________
   Range of mass numbers of Pu isotopes: From _228__ to _ 247 _
   Isotope with the longest half life _244, 8.2e7 y __	Decay (modes): __alpha, beta, EC, SF,____

3. Assume the thermal-neutron induced fission of ²³⁵U (mass = 235.0439) gives two fragments of mass 140 and 93, and the some neutrons. After having consulted the properties of nuclides of mass numbers 140 and 93, we know that ¹⁴⁰Ce (mass = 139.90539) and ⁹³Nb (mass = 92.90638) are stable nuclides. Write the nuclear reaction equation for this fission process. Estimate the total energy (including energies of beta-decay of the fission products) in this fission process.

   Fission reaction:__ ^235U + n ® ^140Ce + 93Nb + 3 n ___

   Energy released: _ Q = __ 200.08 ___ MeV/fission Energy released: _ Q = __ 1.93e13 __ J/mole

4. How much natural uranium must be processed in order to produce 1.0 kg of ²³⁵U, if only 50% of this isotope is extracted from natural uranium? What methods are used to separate ²³⁵U from natural uranium?

   Abundances of ^235U __0.72 %__; ^238U __99.3 % ___

   Amount of natural uranium required: _ 285.7 kg _

   Methods used for extracting ^235U: Gas diffusion of UF6 based on mass difference. _ __ Centrifuging of UF6 gas_____ __ Electromagnetic method to separate UF6^+ ions ___ ___Thermal diffusion __

The following question are provided to help your study, and they will not be marked.

• What is a moderator? What are the desirable properties of a compound to make it a good moderator? Why are heavy water and graphite used as moderator for nuclear reactors using natural uranium as fuel, but normal distilled water not a suitable moderator?

  See the end

• This problem may be a challenge to some of you, but hint will be given on the course website later. Assume the abundance of ²³⁵U to be 5.0% when the earth was created. Calculate the age of the earth from the distribution of ²³⁵U and ²³⁸U (now 0.72 % and 99.28 %). Note that the assumption may not be valid.

  See below

  ---

• What is the percentage of deuterium in natural hydrogen? Assume that 70% of deuterium is extracted from natural water, how much water must be processed in order to produce 1.0 L of heavy water?

  Is it possible to estimate the energy required to produce 1.0 L of heavy water? If it is, how much is required? If not, what information is required or why not?

  Hint
  Deuterium consists of 0.015% of natural hydrogen. To extract 1.0 L heavy water, we carry out the conversion in the following way:

             100 L water   100 %
  1.0 L D2O ------------ ------- = 9524 L water
             0.015 L D2O   70 %
  

  A large amount of water must be processes.

  Many variables are present in the second half of the question, and assumptions have to be made in order to provide answers.

• Assume the abundance of ²³⁵U to be 5.0% when the earth was created. Calculate the age of the earth from the distribution of ²³⁵U and ²³⁸U (now 0.72 % and 99.28 %). Note that the assumption may not be valid.
• What is a moderator? What are the desirable properties of a compound to make it a good moderator? Why are heavy water and graphite used as moderator for nuclear reactors using natural uranium as fuel, but normal distilled water not a suitable moderator?

  Hint
  Assume that at time = 0, the atomic ratio of ₂₃₅U to ₂₃₈U was 5 to 95. After a period of time t, the ratio became 0.72/99.28.

  1. l235 = 0.693/7.038e-8 y = 9.85e-10 y
     l238 = 0.693/4.468e-9 y = 1.55e-10 y

  ²³⁵N = ²³⁵N_o exp (-l₂₃₅ t )
  ----- ---- ------------- dividing the two equations
  ²³⁸N = ²³⁸N_o exp (-l₂₃₈ t )
  Thus,

  0.72    5    exp (-l235 t )
  ---- = ---- --------------- = 0.55 exp -(l235 - l238) t
  99.28  95.0  exp (-l238 t )
  

  0.00725 = 0.55 exp -(l₂₃₅ - l₂₃₈) t Solving for t gives t = 2.4e9 years. (Almost two and half billions years)

  Discussion:
  There are several methods for solving this problem, and all are acceptable. For a period this long, the estimates may be different due to difference in assumptions and methods. The assumption of 5 percent may not be correct, but making it allows us to look at the problem with some values.

Contributors and Attributions

• Chung (Peter) Chieh (Professor Emeritus, Chemistry @ University of Waterloo)