Class 12 Physics · Chapter 13
Short answer: Is chapter me 16 exercise questions cover kiye gaye hain — nuclear composition (isotopes/isobars/isotones), nuclear radius formula R=R0A^(1/3), mass defect aur binding energy calculations (E=Δmc²), binding energy per nucleon curve aur stability, simple half-life/decay-constant numericals, aur fission-fusion Q-value calculations. Chapter numerical-heavy hai — har concept ek calculation ke through samjhaya gaya hai.
Nucleus ek chhota sa, super-dense core hai jisme proton aur neutron paise ki tarah 'bandhe' hote hain — aur unhe bandhe rakhne wali energy hi is chapter ka dil hai. Jab bhi kisi nucleus ka mass measure karte hain, woh uske andar ke individual protons aur neutrons ke total mass se thoda kam nikalta hai — ye 'missing mass' (mass defect) hi Einstein ke E=mc² ke through binding energy banti hai. Binding energy per nucleon ka graph batata hai ki kaunsa nucleus sabse stable hai (iron ke aas-paas), aur isi curve se samajh aata hai ki fission (bade nucleus ko todna) aur fusion (chhote nuclei ko jodna) dono energy kyun release karte hain — dono hi stability ke peak ki taraf badhte hain.
Chapter 13 Summary — 5 Minute Revision
1. Nuclear composition — proton, neutron, aur naming
Nucleus me do types ke particles hote hain, jinhe milakar nucleons kehte hain:
- Proton — positive charge (+e), mass ≈ 1.007276 u
- Neutron — no charge, mass ≈ 1.008665 u (proton se thoda bhaari)
Kisi nuclide AZX ko likhne ka matlab: Z = atomic number = proton count, A = mass number = proton + neutron (total nucleons), aur N = A − Z = neutron count.
| Term | Same kya hai | Different kya hai | Example |
|---|---|---|---|
| Isotopes | Same Z (same element) | Different N (different A) | 1H, 2H, 3H |
| Isobars | Same A | Different Z | 40Ar aur 40Ca |
| Isotones | Same N | Different Z (aur A) | 13C aur 14N (dono N=7) |
↔ Table ko side me swipe karein
2. Nuclear size
Experiments (electron scattering) se pata chala ki nuclear radius mass number A ke cube root ke proportional hota hai:
R = R0A1/3, jahan R0 ≈ 1.2 × 10−15 m
Yahan R0 ≈ 1.2 × 10⁻¹⁵ m (femtometre, fm ya "fermi"). Is formula ka ek important result: nuclear volume A ke proportional hai (V ∝ R³ ∝ A), isliye nuclear density lagbhag har nucleus ke liye SAME hai — chahe A choti ho ya badi. Ye density astronomically high hai (~2.3 × 10¹⁷ kg/m³) kyunki nucleus me almost pura atomic mass ek bahut chhote volume me concentrate hai.
3. Mass-energy equivalence aur mass defect
Agar aap kisi nucleus ke andar ke sabhi protons aur neutrons ka mass alag-alag jodo, toh woh total nucleus ke actual measured mass se zyada nikalta hai. Ye "missing mass" hi mass defect (Δm) kehlata hai:
Δm = [Z·mp + (A−Z)·mn] − Mnucleus
Is missing mass ko Einstein ka mass-energy equivalence relation E=mc² energy me convert karta hai — yahi energy nucleons ko nucleus ke andar bandhe rakhti hai, isliye ise binding energy (BE) kehte hain:
BE = Δm·c² (Δm ko 'u' me rakho toh BE = Δm × 931.5 MeV)
Practical unit conversion: 1 u = 931.5 MeV/c² — isliye jab Δm 'u' me nikale, use seedha 931.5 se multiply karke MeV me BE mil jaati hai.
4. Binding energy per nucleon curve — stability ka master graph
Sirf total BE se stability compare nahi kar sakte (bada nucleus zyada BE dega hi, kyunki usme zyada nucleons hain). Isliye BE per nucleon = BE/A use karte hain — ye batata hai ki AVERAGE ek nucleon kitni tight bandha hai.
- Light nuclei (He, Li) me BE/A kam hai
- Curve A ≈ 56 (iron ke aas-paas) pe peak karta hai — BE/A ≈ 8.7–8.8 MeV/nucleon, sabse stable region
- Heavy nuclei (U-238 jaisi) me BE/A thoda kam ho jaata hai (~7.6 MeV/nucleon)
Isliye: fission (bada, kam-stable nucleus toot kar do medium nuclei banata hai) aur fusion (chhote nuclei jud kar ek medium nucleus banate hain) — dono hi products ka BE/A curve pe peak ke zyada paas le jaate hain, isliye energy release hoti hai.
5. Nuclear force (qualitative)
Protons ek doosre ko electrically repel karte hain (Coulomb force), phir bhi nucleus stable rehta hai — kyunki ek aur, bahut strong nuclear force nucleons ko attract karta hai. Iski key properties:
- Bahut short-range hai (~few fm ke andar hi kaam karta hai, uske baad zero ho jaata hai)
- Charge-independent hai — proton-proton, proton-neutron, neutron-neutron sab pairs pe roughly same strength se kaam karta hai
- Electromagnetic force se bahut zyada strong hai (short range me)
6. Radioactivity (basic idea)
Kuch nuclei unstable hote hain aur apne aap particles/radiation emit karke zyada stable nucleus me convert ho jaate hain — ise radioactive decay kehte hain. Teen main types:
- Alpha (α) decay — nucleus ek helium nucleus (2p+2n) emit karta hai, isliye A ghatta hai 4 se aur Z ghatta hai 2 se
- Beta (β) decay — nucleus ek electron (ya positron) emit karta hai; A same rehta hai, Z ek se badhta/ghatta hai
- Gamma (γ) decay — nucleus high-energy photon emit karta hai (excited state se ground state me aane pe); A aur Z dono same rehte hain
Decay ki rate ko decay constant λ se describe karte hain, aur half-life T½ (jitne time me half sample decay ho jaaye) is formula se related hai:
T½ = 0.693 / λ
Full decay law N = N₀e^(−λt) exist karta hai, par is chapter ka focus deep derivation pe nahi — simple half-life/decay-constant numericals tak hi.
7. Nuclear energy — fission aur fusion
| Fission | Fusion | |
|---|---|---|
| Kya hota hai | Heavy nucleus TOOTTA hai do medium nuclei me | Light nuclei JUDTE hain ek bade nucleus me |
| Example | U-235 + neutron → Ba + Kr + neutrons | Deuterium + Tritium → Helium + neutron |
| Energy per event | ~200 MeV | ~3–18 MeV (reaction pe depend) |
| Trigger condition | Slow neutron capture se chain reaction | Bahut high temperature/pressure chahiye (Sun ke core jaisa) |
↔ Table ko side me swipe karein
Dono reactions me energy Q-value se calculate hoti hai — reactants ka total mass minus products ka total mass, phir 931.5 MeV/u se convert.
Poore Class 12 Physics ke handwritten colour notes
IITian & district toppers ke banaye short notes — revision-ready, diagram ke saath. Board se pehle poora syllabus 3 din me revise.
Exercise Questions — Solutions (Q1–Q16)
Q1. Isotopes, isobars, aur isotones me kya farak hai? Har ek ka ek-ek example do.
Isotopes — same proton number (Z) but different neutron number (isliye different A). Same element ke roop, jaise 1H, 2H (deuterium), 3H (tritium) — sabka Z=1 hai.
Isobars — same mass number (A) but different Z (alag elements). Jaise 40Ar (Z=18) aur 40Ca (Z=20) — dono ka A=40 hai.
Isotones — same neutron number (N) but different Z (aur isliye different A). Jaise 13C (Z=6, N=7) aur 14N (Z=7, N=7) — dono ka N=7 hai.
Q2. Aluminium-27 (27Al) ka nuclear radius calculate karo. (R0 = 1.2 × 10⁻¹⁵ m)
Formula: R = R₀A^(1/3)
R = 1.2 × 10−15 × 271/3
271/3 = 3 (kyunki 3³ = 27)
R = 1.2 × 10−15 × 3 = 3.6 × 10−15 m = 3.6 fm
Q3. Iron-56 (56Fe) ka nuclear radius nikalo.
Formula: R = R₀A^(1/3)
561/3 ≈ 3.826
R = 1.2 × 10−15 × 3.826 ≈ 4.59 × 10−15 m ≈ 4.6 fm
Q4. Do nuclei ke mass numbers 8 aur 216 hain. Unke nuclear radii ka ratio nikalo.
R ∝ A^(1/3), isliye:
R₁/R₂ = (A₁/A₂)1/3 = (8/216)1/3
8/216 = 1/27
(1/27)1/3 = 1/3
Toh R₁ : R₂ = 1 : 3.
Q5. Dikhao ki nuclear density lagbhag sabhi nuclei ke liye same hoti hai, aur uska approximate numerical value nikalo. (mnucleon ≈ 1.66 × 10⁻²⁷ kg, R₀ = 1.2 × 10⁻¹⁵ m)
Mass of nucleus ≈ A × 1.66 × 10⁻²⁷ kg. Volume = (4/3)πR³ = (4/3)πR₀³A (kyunki R³ ∝ A).
Density ρ = mass/volume = [A × 1.66×10−27] / [(4/3)π(R₀)³A]
A dono taraf cancel ho jaata hai — isliye density A pe depend NAHI karti, sabhi nuclei ke liye same hai.
(1.2×10−15)³ = 1.728 × 10−45 m³
(4/3)π × 1.728×10−45 = 7.238 × 10−45 m³
ρ = 1.66×10−27 / 7.238×10−45 ≈ 2.29 × 1017 kg/m³
Q6. Helium-4 nucleus (alpha particle) ki binding energy aur binding energy per nucleon nikalo. (mH = 1.007825 u, mn = 1.008665 u, M(4He) = 4.002603 u)
He-4: Z=2, N=2, A=4.
Δm = [2×1.007825 + 2×1.008665] − 4.002603
= [2.015650 + 2.017330] − 4.002603 = 4.032980 − 4.002603 = 0.030377 u
BE = 0.030377 × 931.5 = 28.30 MeV
BE/A = 28.30/4 = 7.07 MeV/nucleon
Q7. Iron-56 nucleus ki binding energy aur binding energy per nucleon nikalo. (M(56Fe) = 55.934940 u)
Fe-56: Z=26, N=30, A=56.
Δm = [26×1.007825 + 30×1.008665] − 55.934940
= [26.20345 + 30.25995] − 55.934940 = 56.46340 − 55.934940 = 0.528460 u
BE = 0.528460 × 931.5 = 492.26 MeV
BE/A = 492.26/56 ≈ 8.79 MeV/nucleon
Ye value binding-energy-per-nucleon curve ke peak (~A=56) ke bahut paas hai — isliye Fe-56 sabse stable nuclei me se ek hai.
Q8. Uranium-238 nucleus ki binding energy aur binding energy per nucleon nikalo. (M(238U) = 238.050788 u)
U-238: Z=92, N=146, A=238.
Δm = [92×1.007825 + 146×1.008665] − 238.050788
= [92.71990 + 147.26509] − 238.050788 = 239.98499 − 238.050788 = 1.934202 u
BE = 1.934202 × 931.5 ≈ 1801.7 MeV
BE/A = 1801.7/238 ≈ 7.57 MeV/nucleon
Q9. He-4 (7.07 MeV/nucleon), Fe-56 (8.79 MeV/nucleon), aur U-238 (7.57 MeV/nucleon) ki BE/A values diye gaye hain. In values se explain karo ki fission aur fusion dono energy kyun release karte hain.
Fe-56 ka BE/A sabse zyada hai (8.79) — matlab ye sabse stable nucleus hai. He-4 (7.07) aur U-238 (7.57) dono ka BE/A Fe-56 se KAM hai — matlab dono thode kam stable hain, chahe wo ek extreme (bahut halka) ho ya doosra extreme (bahut bhaari) ho.
Fusion: jab halke nuclei (jaise He se bhi halke, H isotopes) jud kar ek medium nucleus banate hain, toh product ka BE/A curve pe UPAR (peak ki taraf) chala jaata hai — is increase ke barabar energy release hoti hai.
Fission: jab U-238 jaisa bhaari nucleus toot kar do medium nuclei banata hai, un products ka BE/A bhi peak ke paas hota hai (U ke 7.57 se zyada) — phir se energy release hoti hai.
Dono process ka common reason: system Fe-56 jaisi peak stability ki taraf move karta hai, aur wahi 'extra' binding energy hi release hoti hai.
Q10. 1 kg U-235 ke complete fission se kitni energy release hogi, agar ek fission event me average 200 MeV energy release hoti hai? (NA = 6.023 × 10²³, 1 MeV = 1.602 × 10⁻¹³ J)
Number of atoms in 1 kg (1000 g) U-235:
N = (1000 g / 235 g·mol⁻¹) × 6.023 × 10²³
= 4.2553 mol × 6.023×10²³ ≈ 2.563 × 10²⁴ atoms
Total energy = N × 200 MeV = 2.563×10²⁴ × 200 = 5.126 × 10²⁶ MeV
In Joules: 5.126×10²⁶ × 1.602×10⁻¹³ ≈ 8.21 × 10¹³ J
Ye lagbhag 82,000 crore Joule hai — ek kilogram U-235 se — jo dikhata hai fission kitni concentrated energy source hai.
Q11. Deuterium-Tritium (D-T) fusion reaction 2H + 3H → 4He + n ka Q-value nikalo. (m(2H)=2.014102 u, m(3H)=3.016049 u, m(4He)=4.002603 u, m(n)=1.008665 u)
Reactants ka total mass:
2.014102 + 3.016049 = 5.030151 u
Products ka total mass:
4.002603 + 1.008665 = 5.011268 u
Δm = 5.030151 − 5.011268 = 0.018883 u
Q = Δm × 931.5 = 0.018883 × 931.5 ≈ 17.59 MeV
Δm positive hai (mass kam hua) isliye reaction exothermic hai — energy release hoti hai, ye Q-value positive hoga.
Q12. Do deuterium nuclei fuse hoke helium-3 aur ek neutron banate hain: 2H + 2H → 3He + n. Q-value nikalo. (m(2H)=2.014102 u, m(3He)=3.016029 u, m(n)=1.008665 u)
Reactants:
2 × 2.014102 = 4.028204 u
Products:
3.016029 + 1.008665 = 4.024694 u
Δm = 4.028204 − 4.024694 = 0.003510 u
Q = 0.003510 × 931.5 ≈ 3.27 MeV
Positive Q-value — energy release hoti hai, magar D-T reaction (Q11) ke comparison me kaafi kam.
Q13. Ek radioactive sample ka half-life 30 din hai. 90 din baad sample ka kitna fraction bacha rahega?
90 din me total half-lives:
n = 90/30 = 3
Remaining fraction = (1/2)ⁿ = (1/2)³ = 1/8 = 0.125
Matlab 90 din baad sirf 12.5% original sample bacha rahega (87.5% decay ho chuka hoga).
Q14. Carbon-14 ka half-life 5730 years hai. Iska decay constant λ nikalo.
Formula:
T½ = 0.693/λ ⟹ λ = 0.693/T½
λ = 0.693 / 5730 ≈ 1.209 × 10−4 per year
Q15. Cobalt-60 (60Co) nuclide ke liye Z, N, aur A identify karo. (Cobalt ka atomic number Z=27 hai)
Notation AX se A seedha diya hota hai:
A = 60, Z = 27 (Cobalt ka atomic number)
N = A − Z = 60 − 27 = 33
Toh Co-60 me 27 protons aur 33 neutrons hain.
Q16. He-4 aur U-238 ke liye fractional mass defect (Δm/M) compare karo, aur explain karo ye binding-energy trend se kaise connect hota hai. (Q6, Q8 ke Δm values use karo: He-4 → 0.030377 u / 4.002603 u; U-238 → 1.934202 u / 238.050788 u)
He-4:
Δm/M = 0.030377 / 4.002603 ≈ 0.00759 (≈ 0.76%)
U-238:
Δm/M = 1.934202 / 238.050788 ≈ 0.00813 (≈ 0.81%)
Dono fractions kaafi close hain, lekin U-238 ka thoda zyada hai He-4 se — lekin BE/A ka trend seedha fractional mass defect se match nahi karta kyunki BE/A = (Δm/M) × M × c²/A ek alag combination hai. Real insight ye hai: total BE/A curve (Q9) hi stability ka sahi measure hai, na ki akela Δm/M ratio.
Important Equations — Ek Nazar Me
| Quantity | Formula | Notes |
|---|---|---|
| Nuclear radius | R = R₀A1/3 | R₀ ≈ 1.2 × 10⁻¹⁵ m |
| Mass defect | Δm = [Z·mp + (A−Z)·mn] − M | M = actual measured nucleus/atomic mass |
| Binding energy | BE = Δm·c² | Δm 'u' me ho toh BE = Δm × 931.5 MeV |
| Mass-energy unit | 1 u = 931.5 MeV/c² | Har numerical me ye conversion factor chahiye |
| Binding energy per nucleon | BE/A | Stability compare karne ka sahi tareeka (total BE nahi) |
| Half-life | T½ = 0.693/λ | λ = decay constant |
| Radioactive decay law | N = N₀e−λt | Existence ke liye stated — is chapter me heavy derivation ka focus nahi |
| Q-value (reaction) | Q = (Σmreactants − Σmproducts) × 931.5 MeV | Q positive = exothermic (energy release), Q negative = endothermic (energy absorb) |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- 931.5 MeV/u conversion bhool jaana. Mass defect Δm 'u' me nikalne ke baad seedha usko MeV bata dena galat hai — hamesha Δm × 931.5 karke MeV me convert karo, warna answer ka order of magnitude hi galat aa jaayega.
- Binding energy aur binding energy per nucleon me confuse ho jaana. Bade nucleus (jaise U-238) ki TOTAL binding energy bahut zyada hoti hai kyunki usme zyada nucleons hain — lekin iska matlab woh zyada stable hai, ye galat conclusion hai. Stability compare karne ke liye hamesha BE/A (per nucleon) dekho, total BE nahi.
- Q-value ka sign ulta laga dena. Q = (reactants ka mass − products ka mass) × 931.5 hai. Agar products ka mass kam hai (mass 'gayab' hua), toh Q positive hai aur reaction exothermic (energy release) hai. Sign ulta karne se exothermic ko endothermic bata doge.
- Fission aur fusion ko mix up karna. Fission me EK bhaari (heavy) nucleus TOOT kar do medium nuclei banata hai (jaise U-235). Fusion me DO ya zyada HALKE (light) nuclei JUD kar ek bada nucleus banate hain (jaise D+T). Reactant/product size dekh kar hi decide karo, na ki sirf naam yaad karke.
- Nuclear radius formula me A ki jagah Z ya mass (kg) daal dena. R = R₀A^(1/3) me A hamesha MASS NUMBER (proton+neutron count) hai, atomic mass in kg/u nahi aur na hi sirf proton number Z. Galat quantity daalne se cube root hi galat aayega.
- Atomic mass aur nuclear mass ko confuse karna. NCERT problems me diya gaya M usually ATOMIC mass hota hai (electrons included), isliye Z proton mass ki jagah Z × hydrogen ATOM ka mass (mH = 1.007825 u) use karte hain — is tarah electron masses dono taraf cancel ho jaate hain. Proton ka bare mass (1.007276 u) use karna without adjustment ek chhoti si consistent error de sakta hai.
Board-Style Important Questions
- 1 mark: Isotopes aur isobars me kya farak hai? Nuclear force ki bhi ek characteristic property likho.
- 2 marks: Mass defect kya hota hai aur ye binding energy se kaise related hai?
- 2 marks: Binding energy per nucleon vs mass number ka graph iron ke aas-paas peak kyun karta hai, ek line me explain karo.
- 3 marks: Kisi diye gaye nuclide (Z, A, atomic mass diya ho) ki binding energy aur binding energy per nucleon calculate karo.
- 3 marks: Fission aur fusion me farak batao, aur ek-ek example reaction likho.
- 5 marks: Ek diye gaye nuclear reaction (fission ya fusion) ka Q-value calculate karo, aur batao ki reaction exothermic hai ya endothermic.
Aksar Poochhe Jaane Wale Sawaal
Nuclear radius formula me R0 ki value kyun 1.2 fm li jaati hai?
Ye ek experimentally determined constant hai — electron scattering experiments se nikala gaya hai. Alag-alag experiments me thoda variation (1.1 se 1.5 fm tak) milta hai, lekin NCERT syllabus ke liye standard value R0 ≈ 1.2 × 10⁻¹⁵ m use karte hain.
Mass defect calculation me hamesha atomic mass (with electrons) kyun use karte hain, nuclear mass kyun nahi?
Kyunki experimentally atomic masses hi easily aur accurately measure hoti hain (mass spectrometry se), nuclear masses nahi. Trick ye hai ki agar Z proton ki jagah Z hydrogen ATOM ka mass use karo, toh dono taraf ke electrons automatically cancel ho jaate hain aur answer sahi aata hai.
Binding energy per nucleon curve me sabse stable nucleus kaunsa hai?
Iron-56 (aur uske aas-paas Ni-62 jaisi nuclei) curve ke peak pe hote hain, BE/A ≈ 8.7-8.8 MeV/nucleon ke saath — ye sabse stable region hai. Isi wajah se stars ke core me fusion Iron tak hi energy release karta hai, uske aage nahi.
Kya radioactive decay ka exact time predict kar sakte hain ki koi ek particular atom kab decay karega?
Nahi. Radioactive decay ek statistical/probabilistic process hai — kisi EK atom ke liye exact decay time predict nahi kar sakte. Lekin bade sample (lakhon-crore atoms) ke liye half-life ek reliable average prediction deta hai ki kitna fraction kitne time me decay hoga.
Fission reactors me energy generate karne ke liye actual reactor design is chapter me cover hota hai kya?
Nahi — current syllabus me nuclear reactor ki construction/working details fully drop kar diye gaye hain. Sirf fission ka basic concept aur Q-value calculation chapter ka scope hai, reactor engineering nahi.
Fusion energy abhi practically use kyun nahi ho rahi, jabki Q-value positive hai?
Fusion ke liye nuclei ko itni close laana padta hai ki unka mutual electric repulsion (Coulomb barrier) overcome ho — iske liye extremely high temperature aur pressure chahiye (jaise Sun ke core me, ya fusion reactors me magnetic/inertial confinement). Ye engineering challenge abhi tak commercially solve nahi hua hai, chahe reaction energetically favorable ho.
Class 12 Physics — Saare Chapters
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