Nuclear Fission & Fusion — Energy released
Nuclei
7
JEE Qs
8%
Hard
75
min
Master the application of mass-energy equivalence (E=mc^2) to calculate the Q-value from mass defects in both fission and fusion reactions, and understand the role of the binding energy per nucleon curve in explaining energy release.
🧮 Key Formulas
✅ Key Points for JEE
- 1Both nuclear fission (heavy nucleus splits into lighter ones) and nuclear fusion (light nuclei combine to form a heavier one) release energy because the resulting daughter nuclei have a higher average binding energy per nucleon compared to the parent nuclei.
- 2The energy released (Q-value) is calculated from the mass defect (Δm = mass of reactants - mass of products) using Einstein's mass-energy equivalence, Q = Δm c^2. A positive Q-value signifies energy release.
- 3The binding energy per nucleon curve fundamentally explains fission and fusion: fission moves heavy nuclei (A > 170) towards the peak of stability (around A=56), while fusion moves light nuclei (A < 20) towards it, both processes resulting in greater stability and energy release.
- 4Fission reactions can be self-sustaining (chain reactions) due to the release of neutrons, which can induce further fission in other nuclei. Critical mass is required to sustain a chain reaction.
- 5Fusion reactions require extremely high temperatures (thermonuclear reactions) and pressures to overcome the strong electrostatic repulsion between positively charged nuclei, allowing them to come close enough for the short-range nuclear force to act.
⚠️ Common Mistakes
- ✕Incorrectly calculating the mass defect by confusing reactants and products, or by making sign errors. Remember Q > 0 for energy released, meaning total reactant mass > total product mass.
- ✕Using inconsistent units or incorrect conversion factor (e.g., forgetting to use 931.5 MeV for 1 amu c^2, or confusing amu with kg without proper conversion).
- ✕Confusing binding energy *per nucleon* with total binding energy when comparing stability or calculating Q-value from BE data. If using binding energies, Q = (Total BE of products) - (Total BE of reactants).
📝 Practice Questions
See allQ32.Choose the correct nuclear process from the below options [p: proton, n : neutron, e− : electron, e+ : positron, v : neutrino, ¯v : antineutrino] (1) n →p + e+ + ¯v (2) n →p + e+ + v (3) n →p + e−+ v (4) n →p + e−+ ¯v
Q40.A radioactive nucleus n2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n1 . If initial number of both nuclei are the same, what is the ratio of number of nuclei of n2 to the number of nuclei of n1 , after one half-life of n1 ? (1) 1/8 (2) 8 (3) 4 (4) 1/4
Q18.Binding energy of a certain nucleus is 18 × 108 J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus: (1) 10μg (2) 20μg (3) 0.2μg (4) 2μg
Q19.Which of the following nuclear fragments corresponding to nuclear fission between neutron (10n) and uranium isotope (23592 U) is correct : (1) 144 56 Ba + 8936Kr + 410n (2) 14456 Ba + 8936Kr + 310n (3) 140 56 Xe + 9438Sr + 310n (4) 15351 Sb + 9941Nb + 310n
Q30.If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is _____ ×10−2MeV . (Given 1u = 931MeV/c2 , atomic mass of helium = 4.002603u )
Q30.The radius of a nucleus of mass number 64 is 4 . 8 fermi. Then the mass number of another nucleus having radius of 4 fermi is 1000 where 𝑥 is _________. 𝑥,
NCERT Chapters
- Class 12 Physics Ch 13: Nuclei