Physics notesOptics & ModernNuclear Physics
Independent topic page
Write N=N₀ e^{−λt} with T_{1/2}=ln2/λ, then mass-defect energy Q = Δm c² for α/β/γ, fission and fusion — keep MeV bookkeeping tight under time pressure.
01. Nucleus: Z protons, N neutrons, A=Z+N. Isotopes share Z. Size scale R≈R₀ A^{1/3}.
02. α: ⁴₂He nucleus emission; β⁻: n→p+e⁻+ν̄; β⁺: p→n+e⁺+ν; γ: electromagnetic de-excitation, Z,A unchanged.
03. Decay law: N=N₀ e^{−λt}; A_activity=λN; T_{1/2}=ln2/λ; mean life τ=1/λ.
04. BE = [Z m_H + (A−Z)m_n − M] c² (careful with atomic vs nuclear masses). Fission/fusion release when products sit higher on BE/A curve.
05. Mass–energy: binding and Q-values live in u and MeV with 1 u ≈ 931.5 MeV/c². Stamp that conversion; never mix u deficit with MeV without it.
06. Decay: N=N₀ e^{−λt}, T_{1/2}=ln2/λ, activity λN. α, β, γ change A/Z by fixed rules—balance nucleon and charge numbers before energetics.
07. Nuclear reactions: conserve A, Z and energy (Q). Fusion vs fission is about binding energy per nucleon curves—stability arguments beat memorised reaction lists.
Official · 2026
Official syllabus points for Nuclear Physics only — not the full Optics & Modern portion map. Portion hub: Optics & Modern · Modern Physics analysis.
No topic-specific exclusions flagged — finish the unit points below for Nuclear Physics.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusNuclear binding, radioactivity, fission/fusion, and decay laws.
Syllabus points
Do / check
2020–2026 paper weight
Topic match inside parent portion Modern Physics (6.8% of Physics tags). Stats below are portion backdrop; matched subtopics show where Nuclear Physics sits.
Portion-wide type/difficulty mix lives on the Modern Physics analysis — not repeated here so this page stays on Nuclear Physics.
01. Dominant subtopics: Atoms/Nuclear/Photoelectric (16).
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Nuclear Physics — practise the knowledge bridge, not only the single-chapter drill.
Step 1: finish photoelectric/nuclear arithmetic cleanly. Step 2: switch to ray-optics formulae (mirror/lens/prism) without reusing constants wrongly. Step 3: track significant figures as required by the grid.
Formula-dense corridor; one wrong sign convention costs two questions.
Keep a tiny optics sign-convention sticky note on your desk during NUM practice.
Why methods matter
Exponential decay, mass-defect MeV conversion and Q-value sharing — convert units before nuclear arithmetic.
Decay-chain MCQs become arithmetic, not memory.
Do thisTrack Z and A column-wise through each emitted particle.
Decay-chain MCQs become arithmetic, not memory.
Two α and one β⁻: A decreases 8, Z decreases 3 net.
Avoids messy e^{−λt} arithmetic under time pressure.
Do thisPrefer N=N₀ / 2^{t/T} when t is a multiple of T_{1/2}.
Avoids messy e^{−λt} arithmetic under time pressure.
After 3 half-lives, N=N₀/8; activity scales the same if λ fixed.
Consistent atomic masses cancel electron masses in many β decays when done carefully.
Do thisQ = (mass initial − mass final) × 931 MeV/u with the mass type the table uses.
Consistent atomic masses cancel electron masses in many β decays when done carefully.
Exothermic decay/fusion ⇒ Q>0 ⇒ products lighter.
Explains energy release without memorising every reaction.
Do thisFission: heavy A toward mid-A; fusion: light nuclei toward mid-A — both raise average BE/A.
Explains energy release without memorising every reaction.
⁴He and mid-iron region are tightly bound; combining or splitting toward them frees energy.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
A sample’s half-life is 10 days. Find the fraction left after 30 days.
This stem rewards early recognition of the radioactive decay law model.
Model chosenN/N₀=(1/2)^{t/T½}.
Answer1/8
Takeaway: Each half-life halves the remaining nuclei.
A nucleus has mass defect 0.1 u. Find its binding energy in MeV.
This stem rewards early recognition of the binding energy and mass defect model.
Model chosen1 u ↔ 931.5 MeV.
Answer≈93.2 MeV
Takeaway: Convert mass defect with 931.5 MeV/u.
In the fusion ²H+³H→⁴He+n, mass excesses give Q=17.6 MeV. If the deuteron and triton approach with negligible KE and the neutron carries 14.1 MeV, find the KE of the α particle.
This Advanced-level variation couples hidden constraints with the fission / fusion q-value model.
Model chosenEnergy and momentum conservation in the CM (approx lab if slow).
Answer3.5 MeV
Takeaway: Q-value sharing follows momentum conservation, not equal split.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likeN=N₀ e^{−λt}; T½=ln2/λ
Fast modelActivity A=λN; mean life τ=1/λ.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeΔm c²; BE per nucleon
Fast modelBE = (Zm_H + (A−Z)m_n − M)c² carefully with units.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeReaction energy from mass excess
Fast modelQ=(Σm_i−Σm_f)c²; positive Q ⇒ exoergic.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeIdentify emission from ΔA, ΔZ
Fast modelα: ΔA=−4, ΔZ=−2; β⁻: Z→Z+1; γ: levels, no ΔZ/ΔA.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline optical elements or modern-physics mode (ray, YDSE/diffraction/polarisation, photoelectric, Bohr, X-ray, nuclear). Note the exact ask and any sign-convention figure.
Write the governing relation once: mirror/lens formula with signs, path difference, Einstein equation, Bohr ΔE, Moseley/de Broglie, or decay law. Reject out-of-syllabus interference setups beyond YDSE.
Compute with one consistent convention and units (eV vs J, nm vs m). Carry magnification signs and decay exponents carefully.
Check limits (thin lens, small angle, λ≪a), energy/sign sense and syllabus scope. Multi-correct: test each statement alone.
After the model is locked
N = N₀ e^{−λt}; A = λN = A₀ e^{−λt}
Radioactive decay
T_{1/2} = ln2/λ; τ = 1/λ; T_{1/2} = τ ln2
Lifetime relations
α: A−4,Z−2; β⁻: Z+1; β⁺: Z−1; γ: A,Z same
Decay identification
Q = Δm c²; 1 u ↔ 931 MeV
Q-value / BE
BE = (Z m_p + N m_n − M_nuc)c² (or atomic form as given)
Nuclear stability energy
BE/A
Stability comparison; fission/fusion drive
1 Ci = 3.7×10¹⁰ Bq (if needed)
Unit conversion
Make it automatic