5.2.8
Radioactive nuclei ek reliable kaam karte hain: woh ek fixed probabilistic rate se decay karte hain jo half-life t 1/2
Clock — count karo kitna decay hua hai → time batao (radiocarbon dating).Tracer/Beam — emit hoti radiation batati hai kahaan (Tc-99m imaging) ya tissue ko destroy karti hai (I-131 therapy).Battery — decay heat → electricity (RTG, Pu-238 spacecraft).
Neeche sab kuch wohi exponential decay law hai jo alag-alag kaam ke liye dress up hua hai.
Definition Radioactive decay lawUn-decayed nuclei N decay ki rate itni hi hoti hai jitne baaki bache hain :
d t d N = − λ N λ decay constant (probability per nucleus per unit time).
Intuition Yeh kaam kyun karta haiCosmic rays upper atmosphere se takraate hain → neutrons banate hain → woh neutrons nitrogen ko radioactive carbon-14 mein convert karte hain:
7 14 N + 0 1 n → 6 14 C + 1 1 p 14 C / 12 C Marne par, intake ruk jaata hai — clock shuru hoti hai. 14 C 6 14 C → 7 14 N + − 1 0 β t 1/2 = 5730
Worked example Ek wooden idol 11.6 counts/min/g deta hai; fresh wood 15.3 counts/min/g deta hai. Age?Step 1 — λ = ln 2/5730 = 1.21 × 1 0 − 4 yr − 1 Kyun? Time mein ratio convert karne ke liye λ Step 2 — ratio A 0 / A = 15.3/11.6 = 1.319 Kyun? Yahi depletion factor hai.
Step 3 — t = 1.21 × 1 0 − 4 1 ln ( 1.319 ) = 1.21 × 1 0 − 4 0.277 ≈ 2290 yr Yeh step kyun? Exponential ko invert karne se marne ke baad beeta hua time milta hai.
Worked example Kitne half-lives baad sirf 25%14 0.25 = ( 1/2 ) n ⇒ n = 2 t = 2 × 5730 = 11460 Kyun? Har half-life amount ko aadha kar deti hai; 25% = do halvings.
Common mistake "Radiocarbon dinosaur bones (65 Myr) ko date kar sakta hai."Kyun sahi lagta hai: carbon sab life mein hota hai, toh ise har jagah kyun nahi use karein?
Fix: ~10 half-lives (~57,000 yr) ke baad itna kam 14 t 1/2 = 4.5
"m" = metastable (ek excited nuclear state). Yeh ek clean gamma photon (140 keV) emit karke relax karta hai — gamma camera ke liye perfect energy — t 1/2 = 6 99 m Tc → 99 Tc + γ ( 140 keV )
Worked example 6 h "just right" kyun haiBahut chhota (minutes): scan se pehle decay ho jaata hai; bahut lamba (days): patient dinon tak irradiated rehta hai. 6 h ⇒ ek-din ke scan ke baad (≈ 4 ( 1/2 ) 4 = 1/16 ≈ 6% Yeh step kyun? Dikhata hai ki dose jaldi self-limit ho jaata hai.
Ek ==destructive β − γ t 1/2 = 8 53 131 I → 54 131 Xe + − 1 0 β + ν ˉ
Intuition Iodine thyroid ko kyun target karta haiThyroid gland naturally iodine concentrate karti hai hormones banane ke liye. Radioactive iodine do → yeh thyroid mein jaata hai → short-range β − overactive ya cancerous thyroid cells ko locally maarta hai bina baki body ko jalaye. Biology targeting ka kaam free mein kar deti hai.
Common mistake "Therapy ke liye bhiγ Kyun sahi lagta hai: γ Fix: γ guzar jaati hai aur bahut kam energy deposit karti hai — imaging ke liye badhiya, maarne ke liye bekar. Therapy ko α / β Diagnosis = penetrating γ β / α
Intuition Solar panels kyun nahi?Voyager, Cassini, New Horizons wahaan udte hain jahan sunlight bahut weak hai. Unhe decades tak steady power chahiye bina kisi moving parts ke aur bina sunlight ke . Solution: ek Radioisotope Thermoelectric Generator (RTG) .
Definition RTG kaise kaam karta hai
Pu-238 α t 1/2 = 87.7 94 238 Pu → 92 234 U + 2 4 α + heat α heat ban jaati hai (~0.56 W per gram).Thermocouples (Seebeck effect) temperature difference (hot Pu vs cold space) ko seedha electricity mein convert karte hain.
Intuition Specifically Pu-238 kyun?
α α 87.7 yr half-life → power decades tak chalti hai (Voyager 1977 mein launch hua abhi bhi chal raha hai!).Pu-239 nahi (woh bomb/reactor isotope hai) — bilkul alag kaam.
Worked example 35 saal baad probe par kitni power bachegi?λ = ln 2/87.7 = 7.90 × 1 0 − 3 yr − 1 = e − λ t = e − 0.2766 = 0.758 ~76% . Yeh step kyun? Heat output ∝ decay rate ∝ N e − λ t
Use
Isotope
Radiation
t 1/2 Kyun choose kiya
Dating
C-14
β − 5730 yr
organics ki age range se match karta hai
Imaging
Tc-99m
γ 6 h
bahar penetrate karta hai, low dose
Therapy
I-131
β − 8 d
thyroid-seeking, locally maarta hai
Power
Pu-238
α 87.7 yr
dense heat, decades ki life
Recall Feynman: 12-saal ke bachche ko samjhaoRadioactive atoms aise hain jaise ice cubes jo ek set speed se pighalni hain. Dating: pata karo ki ek purana cube kitna pighal chuka hai taaki pata chale woh freezer se kitni der pehle nikala gaya. Tc-99m: ek cube jo quietly glow karta hai taaki ek camera tumhare andar ise dhundh sake, phir jaldi pighal jaata hai taaki hurt na kare. I-131: ek cube jo tumhare throat-gland mein baith jaata hai aur paas ki buri cells ko "jalata" hai. Pu-238: ek cube jo 90 saal tak warm rehta hai, aur hum us warmth ko electricity mein convert karte hain Sun se door ek spaceship chalane ke liye.
Mnemonic Isotope ko kaam se match karo"Carbon Counts, Tc Takes-pictures, Iodine Incinerates, Plutonium Powers."
Radiation type rule: "See it = γ β / α
Radiocarbon dating mein "counting" sirf death par kyun shuru hoti hai? Jeevit cheezein atmosphere se 14
Woh nuclear reaction jo atmosphere mein C-14 banati hai? 7 14 N + 0 1 n → 6 14 C + 1 1 p
Activities se age formula? t = λ 1 ln ( A 0 / A ) = l n 2 t 1/2 ln ( A 0 / A )
C-14 dinosaurs ko date kyun nahi kar sakta? ~10 half-lives (~57,000 yr) ke baad almost koi 14
Tc-99m mein "m" ka matlab kya hai? Metastable — ek excited nuclear isomer jo 140 keV gamma emit karke decay karta hai.
Imaging ke liye Tc-99m ideal kyun hai (3 wajah)? Pure penetrating γ
Woh parent isotope jisse Tc-99m generator "milka" jaata hai? Mo-99 (t 1/2 = 66
I-131 specifically thyroid ko kyun treat karta hai? Thyroid naturally iodine concentrate karti hai, isliye I-131 self-target karta hai; iska short-range β −
Imaging vs therapy radiation rule? Imaging ko penetrating γ β / α
RTG mein Pu-238 ka decay? 94 238 Pu → 92 234 U + 2 4 α + heat t 1/2 = 87.7
RTG decay ko electricity mein kaise convert karta hai? α
Spacecraft ke liye Pu-238, Pu-239 kyun nahi? Pu-238 ek long-lived (87.7 yr) α
t 1/2 = ln 2/ λ N = N 0 e − λ t N = N 0 /2 1/2 = e − λ t 1/2 ⇒ ln 2 = λ t 1/2
Radioactive Decay Law — N = N 0 e − λ t Half-life and Decay Constant — kyun har isotope ka t 1/2 Types of Radioactive Decay (alpha, beta, gamma) — penetration decide karti hai diagnose karo ya treat karo.Nuclear Reactions and Transmutation — C-14 aur Pu-238 kaise produce hote hain.Seebeck Effect / Thermocouples — RTG converter ki physics.Activity and Units (Becquerel, Curie) — dating mein hum actually kya measure karte hain.
radiation location or damage
Decay law dN/dt = -lambda N
t = ln A0 over A divided by lambda
