2.3.19 · D1Binding energy — mass defect, BE per nucleon curve
Nucleus protons aur neutrons ka ek tight clump hai, aur us clump ko alag karne mein energy lagti hai — matlab wo clump apne loose pieces se thoda kam weighs karta hai. Is topic mein sab kuch us tiny missing mass ko measure karna hai, use E = m c 2
Parent note padhne se pehle, tumhe wo vocabulary chahiye jo wo quietly assume karta hai. Ye page har ek symbol zero se build karta hai — pehle plain words, phir ek picture, phir kyun is topic ko yeh chahiye . Upar se neeche padho; har block uske upar wale par lean karta hai.
Definition Proton aur neutron — the nucleonsHar atom ke centre mein ek tiny dense ball hoti hai jise nucleus kehte hain. Yeh do tarah ke particles se bani hoti hai:
ek proton — positive electric charge carry karta hai,
ek neutron — koi charge nahi carry karta (neutral).
Saath mein, protons aur neutrons ko nucleons kehte hain ("nucleus mein rehne wali cheezein").
Figure dekho: red balls protons hain, grey balls neutrons hain, sab ek saath crammed hain. Parent note "separated free nucleons" versus "the nucleus" ke baare mein baat karta hai — yeh exactly picture ke right side ke scattered balls aur left side ke clumped balls ka fark hai.
Intuition Clump kyun fly apart nahi kartaSame-charge cheezein repel karti hain. Saare positive protons ko ek doosre ko door dhakhelna chahiye . Kuch zyada strong cheez unhe rok rahi hogi — Strong nuclear force . Woh force hi woh "glue" hai jiske baare mein poora topic actually baat karta hai.
Definition Teen counting numbers
Z atomic number = nucleus mein kitne protons hain. Yeh element ko bhi name karta hai (Z=2 hamesha helium hota hai).N neutron number = kitne neutrons hain.A mass number = nucleons ka total count.
Z A X Z A X Z A 1 2 H → Z = 1 , A = 2 , N = 2 − 1 = 1 ( 1 proton, 1 neutron ) 2 4 He → Z = 2 , A = 4 , N = 2 ( 2 protons, 2 neutrons )
Recall Jaldi self-check92 235 U N = A − Z = 235 − 92 = 143
m p proton ki mass (practically parent m 1 H m n neutron ki mass.M nucleus M atom nucleus (ya atom) ki actually measured mass.
Intuition Picture: ek balance scaleSaare loose nucleons left pan mein rakho aur assembled nucleus right pan mein. Topic ka central surprise yeh hai ki dono pans balance nahi karte — assembled nucleus halka hota hai. Agla figure yeh dikhata hai.
Dono pans ke beech ka gap poore chapter ka star hai. Hum ise §5 mein ek naam dete hain.
Definition Ek special mass unit kyunNucleons absurdly tiny hote hain (ek proton lagbhag 1.67 × 1 0 − 27 atomic mass unit , symbol u 1 u = 12 1 of the mass of one 12 C atom ≈ 1.6605 × 1 0 − 27 kg 1 u 1 u 1.007825 u
u u Atomic mass unit (u) . Topic ko yeh kyun chahiye: har table value aur har worked example u
Δ Δ "koi cheez kitni differ karti hai" ka universal shorthand hai. Toh Δ m fark ."
Common mistake "Defect" ka matlab tuta hua nahi hotaJo galat lagta hai sahi: "defect = flaw = kuch galat hua." Fix: yahan "defect" ka matlab sirf mass ki kami / shortfall hai. Kuch tuta nahi — mass energy mein convert ho gaya (agla section).
E = m c 2 mass Δ m energy chahta hai (woh "glue"). Hume ek aisi bridge chahiye jo mass ko energy mein convert kare. Woh exact bridge Einstein ka Mass–energy equivalence ($E=mc^2$) hai: yeh wahi ek law hai jo kehta hai mass aur energy ek hi cheez ki do currencies hain, fixed exchange rate c 2
E = m c 2
E m c c ≈ 3 × 1 0 8 m/s c 2
Definition Binding energyBinding energy E B deni padti hai ek nucleus ko free nucleons mein wapas todne ke liye (utni hi energy release hoti hai jab woh pehli baar saath aate hain). §5 aur §6 se:
E B = Δ m c 2
Intuition Energy-well pictureFigure mein, free nucleons upar baithte hain (high energy). Jaise jaise woh nucleus mein saath aate hain, woh ek well mein gir jaate hain — us well ki gehraai hi E B E B
Definition Binding energy per nucleonKisi symbol par bar ka matlab "average" hota hai. Toh
E B = A E B per nucleon " — total glue saare A Topic ko yeh kyun chahiye: total E B A
BE per nucleon E_B over A
Stability and the BE curve
Fusion and Fission release energy
Upar se neeche padho: counts aur masses mass defect dete hain, mass–energy bridge use binding energy mein convert karta hai, A per-nucleon score milta hai, aur woh score stability curve explain karta hai — aur isliye Nuclear fusion aur Nuclear fission bhi.
Khud test karo — tum parent note ke liye tabhi ready ho jab har reveal instantly aaye.
Nucleons kya hote hain, aur kaunsa charged hota hai? Protons aur neutrons; proton positively charged hota hai, neutron neutral hota hai.
Z N A Z N A A = Z + N N = A − Z
Z A X Bottom-left Z A = A − Z
1 u Ek 12 ≈ 1.66 × 1 0 − 27
Δ Δ m Δ Δ m
Assembled nucleus apne parts se halka kyun hota hai? Use assemble karne se binding energy release hoti hai jo system se bahar chali jaati hai, toh E = m c 2
Topic mein use hone wala mass→energy conversion batao. 1 u c 2 = 931.5 E B = Δ m ( in u ) × 931.5
E B Woh energy jo ek nucleus ko free nucleons mein todne ke liye chahiye (ya jab woh combine hote hain tab release hoti hai).
E B A "Average"; total E B A
