Nuclear Energy: Quick, Friendly Notes 🚀
1. Binding Energy and the Big Picture 🔗
Plot the binding energy per nucleon \(E_{bn}\) against mass number \(A\). Between \(A = 30\) and \(A = 170\) the curve stays almost flat at \(8.0\;\text{MeV}\) per nucleon. For lighter nuclei (\(A<30\)) and heavier nuclei (\(A>170\)) the value drops below \(8.0\;\text{MeV}\). When nuclei move from a low-\(E_{bn}\) region to a high-\(E_{bn}\) region they release energy—that’s the heart of both fission and fusion! :contentReference[oaicite:0]{index=0}
Because a bound system with greater \(E_{bn}\) has less total mass, any change that increases \(E_{bn}\) spits out energy. That explains why a heavy nucleus splitting or two light nuclei merging both deliver huge energy pay-offs. :contentReference[oaicite:1]{index=1}
For scale, breaking 1 kg of uranium unleashes \(10^{14}\,\text{J}\). Burning 1 kg of coal yields only \(10^{7}\,\text{J}\). That’s a million-fold advantage! ⚡ :contentReference[oaicite:2]{index=2}
2. Fission: Splitting the Heavyweights 💥
Key reaction
The classic neutron-induced split:
\[ {}^{1}_{0}\text{n}+{}^{235}_{92}\text{U}\rightarrow{}^{236}_{92}\text{U}\rightarrow{}^{144}_{56}\text{Ba}+{}^{89}_{36}\text{Kr}+3\,{}^{1}_{0}\text{n} \tag{13.10} \]
Other fragment pairs also show up, e.g.
\[ {}^{1}_{0}\text{n}+{}^{235}_{92}\text{U}\rightarrow{}^{236}_{92}\text{U}\rightarrow{}^{133}_{51}\text{Sb}+{}^{99}_{41}\text{Nb}+4\,{}^{1}_{0}\text{n} \tag{13.11} \]
\[ {}^{1}_{0}\text{n}+{}^{235}_{92}\text{U}\rightarrow{}^{140}_{54}\text{Xe}+{}^{94}_{38}\text{Sr}+2\,{}^{1}_{0}\text{n} \tag{13.12} \]
Each fissioning nucleus releases roughly \(200\;\text{MeV}\). Here’s a neat estimate for a nucleus with \(A = 240\) splitting into two \(A = 120\) pieces:
- \(E_{bn}\) (parent) ≈ \(7.6\;\text{MeV}\)
- \(E_{bn}\) (each fragment) ≈ \(8.5\;\text{MeV}\)
- Gain per nucleon ≈ \(0.9\;\text{MeV}\)
- Total gain ≈ \(240 \times 0.9 = 216\;\text{MeV}\)
The kinetic energy of fragments and free neutrons quickly turns into heat—the power behind reactors ⚙️ and the blast of an atom bomb 💣. :contentReference[oaicite:3]{index=3}
3. Fusion: Power of the Stars ☀️
Sample fusion reactions
\[ {}^{1}_{1}\text{H}+{}^{1}_{1}\text{H}\rightarrow{}^{2}_{1}\text{H}+e^{+}+ν+0.42\,\text{MeV} \tag{13.13a} \]
\[ {}^{2}_{1}\text{H}+{}^{2}_{1}\text{H}\rightarrow{}^{3}_{2}\text{He}+n+3.27\,\text{MeV} \tag{13.13b} \]
\[ {}^{2}_{1}\text{H}+{}^{2}_{1}\text{H}\rightarrow{}^{3}_{1}\text{H}+{}^{1}_{1}\text{H}+4.03\,\text{MeV} \tag{13.13c} \]
Coulomb barrier 🚧
Nuclei repel because of their positive charge, so they must zoom in with about \(400\;\text{keV}\) each (for two protons) to beat the barrier—that’s a temperature of roughly \(3\times10^{9}\;\text{K}\)! :contentReference[oaicite:4]{index=4}
The proton-proton (p-p) chain in the Sun
Inside the Sun (core temperature \(1.5\times10^{7}\;\text{K}\)) rare high-energy protons trigger a four-step loop:
- \({}^{1}_{1}\text{H}+{}^{1}_{1}\text{H}\rightarrow{}^{2}_{1}\text{H}+e^{+}+ν+0.42\;\text{MeV}\) (twice)
- \(e^{+}+e^{-}\rightarrow γ+γ+1.02\;\text{MeV}\) (twice)
- \({}^{2}_{1}\text{H}+{}^{1}_{1}\text{H}\rightarrow{}^{3}_{2}\text{He}+γ+5.49\;\text{MeV}\) (twice)
- \({}^{3}_{2}\text{He}+{}^{3}_{2}\text{He}\rightarrow{}^{4}_{2}\text{He}+{}^{1}_{1}\text{H}+{}^{1}_{1}\text{H}+12.86\;\text{MeV}\)
Net effect:
\[ 4\,{}^{1}_{1}\text{H}\rightarrow{}^{4}_{2}\text{He}+2\,e^{+}+2\,ν+γ+26.7\;\text{MeV} \tag{13.15} \]
This chain keeps our Sun shining for ~\(5\times10^{9}\) more years 🌞.
4. Controlled Thermonuclear Fusion 🔒
On Earth we heat deuterium-tritium or similar fuel to about \(10^{8}\;\text{K}\) so it becomes a plasma—a soup of ions and electrons. The big challenge is to hold this ultra-hot plasma without melting the container. Magnetic “bottles” and inertial confinement aim to do the trick. Success could give us practically limitless clean power. 🤞 :contentReference[oaicite:5]{index=5}
5. Conservation Rules & Mass–Energy Magic ✨
Nuclear equations balance proton number and neutron number separately. Elements can change, but these counts stay put. Energy appears because the total binding energy—and therefore total mass—differs between the reactants and products. Even chemical reactions do this, but their mass defects are about a million times smaller. :contentReference[oaicite:6]{index=6}
High-Yield Ideas for NEET 📚
- The shape of the \(E_{bn}\) vs \(A\) curve and why energy releases during fission and fusion. :contentReference[oaicite:7]{index=7}
- Standard U-235 fission equation with free neutrons and ~\(200\;\text{MeV}\) output. :contentReference[oaicite:8]{index=8}
- Coulomb barrier concept and required temperature (\(3\times10^{9}\;\text{K}\)) for thermonuclear fusion. :contentReference[oaicite:9]{index=9}
- Net p-p cycle reaction that powers the Sun and releases \(26.7\;\text{MeV}\). :contentReference[oaicite:10]{index=10}
- Conservation of protons and neutrons in nuclear reactions and the link to mass–energy interconversion. :contentReference[oaicite:11]{index=11}
Keep exploring and let the energy of the nucleus spark your curiosity! 🌟
