Ch7: Nuclear Energy and Reactions

Class Opinions & Public Perception

• Instructor opens by gauging student attitudes toward nuclear energy

• Mixed responses: “very powerful,” “efficient,” but also “unsafe” due to past accidents (student recalls an “island” rendered uninhabitable—likely Three Mile Island, Chernobyl, or Fukushima)

• Key takeaway: society is split between pro- and anti-nuclear stances, largely hinging on perceived risk

• Instructor stresses the decision framework:

  • Never consider nuclear in isolation; always ask “What is the alternative?”

  • Energy choices are fundamentally a risk–benefit analysis

Fundamental Nuclear Reactions

• Two broad nuclear processes exist

  • Nuclear fission (focus of this lecture)

  • Definition: splitting a large nucleus into smaller nuclei

  • Dominant process in commercial power plants & most “atomic” bombs

  • Nuclear fusion (briefly mentioned)

  • Definition: combining small nuclei to form a larger nucleus

  • Relevant for hydrogen bombs and experimental power concepts, not typical reactors discussed here

Canonical Fission Equation

• Example reaction used throughout: $^{235}<em>{92}U + ^1</em>0n \;\longrightarrow\; ^{141}<em>{56}Ba + ^{92}</em>{36}Kr + 3\, ^1_0n + \text{energy}$

• Left-hand side (reactants): $^{235}_{92}U$ plus a neutron

• Right-hand side (products): barium-141, krypton-92, three additional neutrons, and a large energy release

• Sub- and superscript bookkeeping (approximate mass/atomic number conservation):

  • Superscripts (mass numbers): $235 + 1 = 236$ on reactants; $141 + 92 + 3\times1 = 236$ on products

  • Subscripts (atomic numbers): $92 + 0 = 92$ on reactants; $56 + 36 + 0 = 92$ on products

• Decimal-level mass is lost ($\sim0.1 \%$), but it hides in the un-written digits (e.g., $^{235}U$ actually $\approx 235.043924 \text{ u}$)

Mass–Energy Relationship

• Einstein’s equation underpins nuclear energy output: $E = m c^2$

• $c$ = speed of light \approx 3.00 \times 10^8\,\text{m\cdot s}^{-1} — a very large constant, so even tiny $\Delta m$ yields enormous $\Delta E$

• In fission $\sim0.1 \%$ of the original mass converts directly to energy

• Instructor notes many scientists still marvel at this matter \rightarrow energy conversion

Chain Reactions & Critical Mass

• Fission of $^{235}U$ releases additional neutrons \rightarrow these neutrons can strike more $^{235}U$, propagating a chain reaction

• Critical mass = minimum mass of fissile material that makes the chain reaction self-sustaining

  • For $^{235}U$: $\approx \textbf{15 kg}$ ($\approx \textbf{33 lb}$)

  • Below this threshold, too many neutrons escape; reaction fizzles out

• Self-sustaining chains are exploited in power reactors & weapons; controlling the neutron population is central to safety design

Neutron Sources / Generators

1. Secondary neutrons from fission itself

   • The 3 neutrons in the canonical equation perpetuate the reaction

2. ($\alpha$,n) Reactions (alpha particle hits light nucleus)

   • Example (details simplified):

   $^{238}<em>{94}Pu \;\longrightarrow\; ^4</em>2\alpha + \dots$ \rightarrow the $\alpha$ then bombards $^9<em>4Be$ $^4</em>2\alpha + ^9<em>4Be \;\longrightarrow\; ^{12}</em>6C + ^1_0n + \gamma$

• Net result: free neutron production plus $\gamma$-radiation (pure electromagnetic energy)

1. Fusion-based neutron generators

   • Deuterium–tritium reaction:

   $^2<em>1H + ^3</em>1H \;\longrightarrow\; ^4<em>2He + ^1</em>0n + \text{energy}$$

Quantifying Uranium Usage & Energy Output (Preview)

• Instructor promises a worked calculation later showing how small masses of uranium yield huge energies

• Key hint: conventional fuels (coal, oil) release a few kJ per gram; fission releases millions of kJ per