Unit 11 : Additional Problems

Unit 11 : Additional Problems#

For those looking for additional problems outside of past exam questions and the worked problems in the lectures please consider the following in the reading list.

Quick Problems#

  1. Fill in the blanks in these fission reactions and calculate their Q-values:

  • \( ^{235}U + n \to ^{90}Kr + ^{144}Ba + ? \);

  • \( ^{239}Pu + \gamma \to ^{92}Sr + ? + 3n \);

  • \( ^{252}Cf \to ^{106}Nb + ? + 4n \).

  1. \( ^{252}Cf \) has a half-life of \( 2.64 \, \text{years} \) and a branching ratio for spontaneous fission of \( 3.09\% \). On average, each fission produces \( 3.76 \, \text{neutrons} \). How many neutrons per second are emitted by \( 1 \, \text{mg} \) of \( ^{252}Cf \)?

  2. The distribution of the actual number of neutrons emitted per fission is remarkably Gaussian (see Krane, figure 13.7) with a standard deviation of \( 1.08 \). If the mean number of neutrons produced in the fission of \( ^{235}U \) is \( 2.42 \), what is the probability that a fission of \( ^{235}U \) will produce no neutrons?

  3. Which of the following heavy nuclei would you expect to have large thermal neutron cross sections? Justify your answers:

  • \( ^{251}Cf \);

  • \( ^{253}Es \);

  • \( ^{255}Fm \);

  • \( ^{250}Bk \).

Unworked Example : Proton-Boron Fusion Reaction#

The reaction \( p + ^{11}B \to 3\alpha \) is sometimes considered for commercial fusion. Its advantages include all charged products and \( ^{11}B \) being stable and abundant (80% of natural boron).

  1. What is the \( Q \)-value of this reaction?

  2. What is the Gamow energy for this reaction?

  3. Compare the Gamow energy for this reaction with that of d-t fusion.

  4. Explain, as quantitatively as possible, why this reaction is unlikely to be used in commercial fusion reactors in the foreseeable future.

Relevant atomic mass:

  • \( ^{11}B \): 11.0093052 u

Relevant particle masses:

  • Proton (\( p \)): 1.0072765 u

  • Neutron (\( n \)): 1.0086649 u

  • Deuterium (\( d \)): 2.0135532 u

  • Tritium (\( t \)): 3.0155007 u

  • Alpha particle (\( \alpha \)): 4.0015062 u.

Additional Questions to consider#

  • Write an example induced fission reaction.

  • Explain the terms critical, subcritical, and supercritical.

  • How do control rods work in a reactor?

  • What are alpha-n reactions and give an example neutron source using these.

  • What conditions would give maximum transfer of energy between a projectile and target particle.

  • Write an example non-elastic reaction.

  • Explain threshold reactions.

  • What are fasst neutrons?

  • Derive an equation for the maximum released energy in a fission reaction.

  • What is it about neutrons in fission that allows steady chain reactions?

  • Explain the terms critical mass, super criticality and prompt critical.

  • What moderator is ussed in a Magnox reactor?

  • How might the energy output per gram compare between fission and fusiono?

  • Write out the DT reaction equation.

  • Why is DT favoured over DD for a fusion power reactor.

  • Explain gravitational confinement in fusion, where does it occur?

  • What is a Tokoamak?

  • Derive the Lawson Criteria and explain it’s importance in fusion reactors.

  • What is a breeding blanket in a fusion reactor?