2.3.20 · D1Nuclear reactions — Q-value calculation
Ek nuclear reaction ek tarazu ka khel hai: pehle sab kuch tolo, baad mein sab kuch tolo, aur jo thodi si mass gayab ho gayi woh energy ban ke wapas aati hai. Parent page par har symbol — m c 2 Q K Δ m Z A X
Yeh page parent Q-value note ki har notation ka piece build karta hai, ek aisi reader se shuru karke jisne inhe kabhi nahi dekha. Upar se neeche padho: har symbol earn kiya jaata hai pehle, tab dusra uska sahara leta hai.
Kuch bhi tolne se pehle, hume usse naam dena hoga. Ek nucleus ko Z A X
Z A X
X chemical symbol (H, He, N, O, Po…) — batata hai kaun sa element hai.Z atomic number (bottom-left) = protons ki sankhya. Yeh yeh bhi fix karta hai ki ek neutral atom mein kitne electrons hain.A mass number (top-left) = protons aur neutrons ki sankhya (inhe milake nucleons kehte hain).Toh neutron count hai N = A − Z
Figure dekho: nucleus ek baag mein balls ki tarah hai. Blue balls = protons (inki sankhya Z pale balls = neutrons (inki sankhya A − Z total count A A Z
Intuition Topic ko yeh kyun chahiyeEk reaction a + X → Y + b inhi balls ko rearrange karta hai. Yeh check karne ke liye ki kuch bhi naya create nahi hua, hum balls count karte hain: pehle total Z Z A A
Worked example Do real examples padhna
2 4 He Z = 2 A = 4 N = 4 − 2 = 2 alpha particle hai.0 1 n Z = 0 A = 1 neutron .
m m rest mass (jab woh bilkul still hai toh uski mass). Hum nuclear masses ek tailor-made unit mein maapte hain.
Definition Atomic mass unitu 1 u 12 u 1 u = 1.6605 × 1 0 − 27 kg suvidha hai — nuclear masses chote saaph numbers mein aati hain jaise 2.014102 u 1 0 − 27
Intuition Kilograms kyun nahi?Ek proton ka weight lagbhag 0.0000000000000000000000000017 u 1.007
Yeh puri topic ka sar hai: mass aur energy alag currencies mein ek hi cheez hain, aur c
c c 2 c = 2.998 × 1 0 8 m/s speed of light — nature ka ek fixed constant. Yeh squared appear karta hai kyunki energy speed squared ke saath scale karti hai (jaise kinetic energy 2 1 m v 2 c 2
Full story ke liye dekho Mass-energy equivalence E=mc^2 । Hamare liye, c 2 gayab hua mass multiply karo to milti hai energy jo saamne aayi.
c 2 E = m c 2 c 2 missing mass × c 2 = energy released
Pichhle do sections ko milane se parent page par sabse zyada use hone wala number milta hai.
931.5 1 u E = m c 2
E = ( 1.6605 × 1 0 − 27 kg ) ( 2.998 × 1 0 8 m/s ) 2 = 1.4924 × 1 0 − 10 J = 1.602 × 1 0 − 13 J/MeV 1.4924 × 1 0 − 10 J = 931.5 MeV
eV MeV 1 eV 1 1.602 × 1 0 − 19 J 1 MeV = 1 0 6 eV MeV mein hoti hain, isliye hum isme convert karte hain.
Ab: mass kyun gayab hoti hai? Kyunki ek bound nucleus apne loose parts se halka hota hai.
Δ m halka hai. Yeh kami mass defect hai, aur Δ m c 2 binding energy hai — woh energy jo aapko nucleus ko wapas alag karne ke liye pump karni padegi. Dekho Binding energy and mass defect .
Figure mein loose balls upar baithti hain (bhaari, unbound); ek baar snap ho jaayein toh woh ek kue mein gir jaati hain (halki, bound). Kue ki gehraai binding energy hai.
Intuition Topic ko yeh kyun chahiyeEk reaction balls ko ek nayi kue mein rearrange karta hai jo alag gehraai ki hai. Agar products ek zyada gehri kue mein baithein (zyada tightly bound), toh extra mass free hoti hai aur energy ke roop mein bahar aati hai — ek positive Q
Common mistake Binding energy meinΔ m Q Δ m Δ m ek nucleus ka mass defect, aur (b) poori reaction ka mass change . Q-value page par, Δ m = m before − m after
Free hui energy hawa mein gayab nahi hoti; yeh products ki motion ban jaati hai.
Definition Kinetic energyK K chal raha hai . c K = 2 1 m v 2 K = ( total energy ) − m c 2 K a , K X , K Y , K b
p p = m v ek direction mein point karti hai . Iska key property: ek isolated system ka total momentum kabhi nahi badalta. Dekho Conservation of momentum in decays .
Figure dekho. Ek rest par parent ka zero total momentum hai. Split hone ke baad, dono fragments ko equal-and-opposite momenta ke saath door jaana chahiye taaki arrows abhi bhi cancel ho ke zero hojayein. Isliye hi heavy daughter ko recoil karna padta hai — aur baad mein koi bhi fragment bilkul rest par nahi reh sakta.
Ab parent ki headline formula ka har symbol define ho gaya hai:
Reactions (Alpha decay , Beta decay , Nuclear fission , Nuclear fusion ) jo bhi karte hain, woh sab is ek bookkeeping line ka special case hai.
Count protons and neutrons
Right side cover karo aur khud test karo — parent page ke liye aap tabhi ready hain jab inhe saare answer de sako.
Z A X A Z A Z
7 14 N N = A − Z = 14 − 7 = 7
1 u u 1.6605 × 1 0 − 27 kg
E = m c 2 c 2 Yeh exchange rate hai jo rest mass ko uski equivalent energy mein badalta hai; bada kyunki c
1 u 1 u = 931.5 MeV / c 2 u 931.5
Kisi nucleus ka mass defect Δ m (Free nucleon masses ka sum) − (actual nucleus mass); yeh positive hai kyunki bound nuclei halke hote hain.
Ek decay mein daughter nucleus ko recoil kyun karna padta hai? Rest par parent ka zero momentum hota hai; fragments ko equal-and-opposite momenta carry karna hoga taaki total zero rahe.
Q-value ke dono faces likho. Q = Δ m c 2 = K final − K initial
