2.3.24
Fusion woh process hai jo Sun ko power deti hai: chote nuclei aapas mein takraate hain ek bada nucleus banane ke liye, aur kyunki product zyada tightly bound hoti hai, bacha hua mass energy ke roop mein release hota hai (E = m c 2 repel karte hain — isliye tumhe insane temperatures chahiye (millions of kelvin) taaki unhe itna paas laaya ja sake ki strong force control le sake. Ek tokamak humanity ki koshish hai ki us hot, dense plasma ko Earth par recreate kiya jaye aur magnetic fields se use rokke rakha jaye.
Intuition Binding-energy curve par chadnaHar nucleus ki ek binding energy per nucleon B / A 56 Fe
Peak se neeche (light nuclei): unhe join karna tumhe curve par upar le jaata hai → product zyada tightly bound → energy release hoti hai. Yeh hai fusion .Peak se upar (heavy nuclei): unhe todna tumhe upar le jaata hai → fission .
Toh fusion sirf light nuclei ke liye energy release karta hai (iron se neeche).
Definition Nuclear fusionWoh process jahan do light nuclei combine hokar ek heavier nucleus banate hain, energy release karte hue kyunki product ki binding energy per nucleon reactants se zyada hoti hai.
KYA chahiye: woh energy Q
KYUN kaam karta hai: mass exactly conserved nahi hota — product reactants ke sum se halka hota hai. Woh "missing mass" Δ m
KAISE — key reaction 1 2 D + 1 3 T → 2 4 He + n
Reactants ka total rest mass = m D + m T Kyun? Energy rest mass mein locked hoti hai.
Products ka total rest mass = m H e + m n
Mass defect: Δ m = ( m D + m T ) − ( m H e + m n ) Kyun subtract? Mass mein jo kami aayi woh convert ho gayi.
Energy released:
Q = Δ m c 2 Kyun c 2 Einstein ki mass–energy equivalence: ek tiny mass times huge number c 2
Intuition Sun kyun slow aur steady haiSun ka core sirf ~1.5 × 1 0 7 bahut thanda hai! Fusion ho bhi paata hai toh sirf quantum tunnelling ki wajah se jo Coulomb barrier ke through hota hai — aur tab bhi, pehle step ke liye weak force chahiye, jo rare hai. Wahi slowness ki wajah se Sun billions of years se jal raha hai explode hone ki jagah.
P–p chain ka net result:
4 1 1 H → 2 4 He + 2 e + + 2 ν e + energy
KAISE chain chalti hai (concept level):
p + p → 2 D + e + + ν e bottleneck (weak interaction, bahut slow). Kyun slow? Ek proton ko weak force ke zariye neutron mein turn karna padta hai.2 D + p → 3 He + γ 3 He + 3 He → 4 He + 2 p
Intuition Teen cheezein hain jinhe tumhe beat karna hai
Coulomb repulsion → fuel ko ~1 0 8 Koi wall touch nahi kar sakti → plasma ko magnetic fields se confine karo taaki woh chamber se na takraye.Kaafi der aur kaafi dense rakho → Lawson criterion .
Ek toroidal (doughnut-shaped) chamber jo hot plasma ko magnetic fields use karke confine karta hai, taaki controlled nuclear fusion achieve ho sake. Charged particles field lines ke saath spiral karte hain, toh ek clever twisted (helical) field unhe escape kiye bina circulate rakhta hai.
Matter ki fourth state: ek gas itni hot ki electrons ukhad jaate hain, peechhe ek soup of free ions and electrons chodkar. Kyunki yeh charged hai, yeh magnetic fields par respond karta hai — yahi magnetic confinement ko possible banata hai.
Ek charged particle magnetic field mein Lorentz force F = q v × B perpendicular hoti hai → yeh particle ko field lines ke around circle karaati hai (gyration) unhe cross karne ki jagah. Yeh kyun help karta hai: particles field lines se tied hote hain, toh field ko ek closed loop (torus) mein bend karke, tum unhe trap kar lete ho.
Worked example 1 — D–T fusion energy2 D + 3 T → 4 He + n m D = 2.014102 m T = 3.016049 m H e = 4.002603 m n = 1.008665 Q
Step 1: Reactant mass = 2.014102 + 3.016049 = 5.030151 Kyun? Inputs ko sum karo.
Step 2: Product mass = 4.002603 + 1.008665 = 5.011268 Kyun? Outputs ko sum karo.
Step 3: Δ m = 5.030151 − 5.011268 = 0.018883 Kyun subtract? Yahi mass lost hua → energy.
Step 4: Q = 0.018883 × 931.5 = 17.6 Kyun ×931.5? u·c 2
Result: Q ≈ 17.6 MeV
Worked example 2 — D–T over D–D kyun?D–T 17.6 MeV release karta hai; D–D ~3–4 MeV release karta hai aur aur bhi hotter plasma chahiye. Yeh step kyun matter karta hai: D–T ka sabse lowest temperature par largest cross-section hai, toh ignite karna sabse aasaan hai — isliye ITER ise use karta hai despite tritium ke radioactive hone ke.
Worked example 3 — Sun ki mass loss rateSun L = 3.8 × 1 0 26 Step 1: E = m c 2 ⇒ m ˙ = L / c 2 Kyun? Radiated energy mass se aayi.
Step 2: m ˙ = ( 3 × 1 0 8 ) 2 3.8 × 1 0 26 = 4.2 × 1 0 9 Result: Sun ~40 lakh tonne per second lose karta hai — phir bhi billions of years jeeta hai (uska mass 2 × 1 0 30
Common mistake "Fission aur fusion dono nuclei ko split karke energy release karte hain."Kyun sahi lagta hai: Dono nuclear hain aur dono energy release karte hain, toh log unhe ek saath lump kar dete hain. Fix: Fusion light nuclei ko join karta hai (iron se neeche); fission heavy nuclei ko split karta hai (iron se upar). Dono B / A move karte hain — yahi unifying idea hai.
Common mistake "Sun itna hot hai, toh fusion easy hai."Kyun sahi lagta hai: 1 0 7 Fix: Classically yeh Coulomb repulsion overcome karne ke liye kaafi nahi hai — solar fusion sirf quantum tunnelling ki wajah se hota hai, aur rate per proton bahut tiny hai. Sun isliye shines karta hai kyunki uske paas enormous number of protons hain, na ki isliye ki har reaction fast hai.
Common mistake "Ek tokamak ko Sun se zyada temperature chahiye kyunki woh better hai."Kyun sahi lagta hai: Better tech = zyada extreme, zaroor. Fix: Humein zyada T isliye chahiye kyunki humare paas Sun ki gravity nahi hai jo plasma ko compress aur confine kare. Gravity jo free mein karta hai, woh hume heat aur magnets se brute-force karna padta hai.
Common mistake "Magnetic field plasma ko energy deta hai / usse work karta hai."Kyun sahi lagta hai: Woh plasma ko control karta hai, toh zaroor use push karta hoga. Fix: F = q v × B v zero work karta hai — woh sirf redirect (confine) karta hai, kabhi heat nahi karta. Heating currents, RF waves, aur beams se aati hai.
Recall Feynman: ek 12-saal ke bachche ko samjhaoSun light banata hai chote hydrogen bits ko saath mein smoosh karke helium banane ke liye. Jab woh stick karte hain, unka thoda sa weight gayab ho jaata hai aur ek BADI energy burst mein badal jaata hai — yahi hai E = m c 2
"Light Loves to Lump, Heavy Halves" — L ight nuclei → fuse (lump together); H eavy nuclei → fission (halve apart). Dono iron ki taraf climb karte hain.
Tokamak essentials ke liye: "Hot, Held, Hopeful" = H eat (1 0 8 H eld (magnetic torus), H opeful (Lawson triple product).
Light nuclei ka fusion energy kyun release karta hai? Product ki binding energy per nucleon zyada hoti hai; lost mass Δ m Q = Δ m c 2
Solar p–p reaction ka net result kya hai aur uski energy? 4 1 H → 4 He + 2 e + + 2 ν e , releasing
26.7 MeV.
Sun ka core (1.5×10⁷ K) "too cold" hone ke bawajood fusion kar paata hai, kyun? ::: Coulomb barrier ke through quantum tunnelling.
ITER jaise reactors kaun si reaction use karte hain aur uski Q-value kya hai? ::: D–T fusion, 2 D + 3 T → 4 He + n Q ≈ 17.6 F = q v × B n T τ E 3 × 1 0 21 keV·s/m³ for D–T) se zyada hona chahiye net energy gain ke liye.
Tokamak Sun ke core se zyada hot kyun hona chahiye? Uske paas Sun ka gravitational compression nahi hai, isliye fusion drive karne ke liye zyada temperature chahiye.
Plasma kya hai? Ek hot ionised gas of free electrons aur ions, jo magnetic fields par respond karta hai.
Fusion vs fission: iron peak ke kaunsi side? Fusion = light nuclei below iron; fission = heavy nuclei above iron.
Binding Energy per Nucleon Curve — explain karta hai kyun dono fusion aur fission energy release karte hain.Mass-Energy Equivalence (E=mc^2) — released energy ka source.Nuclear Fission — heavy nuclei ke liye complementary process.Lorentz Force — magnetic confinement ki basis.Quantum Tunnelling — kyun Sun low core temperature ke bawajood fuse karta hai.Plasma — Fourth State of Matter
Binding energy per nucleon curve
Q value = mass defect x c2
Millions of kelvin plasma