Binding Energy — Mass defect, BE per nucleon
Nuclei
7
JEE Qs
8%
Hard
75
min
Master the calculation of mass defect and binding energy, and thoroughly understand the binding energy per nucleon curve to predict energy release in nuclear reactions.
🧮 Key Formulas
✅ Key Points for JEE
- 1Mass defect (Δm) is the difference between the sum of masses of individual nucleons (protons and neutrons) and the actual mass of the nucleus. This 'missing mass' is converted into binding energy.
- 2Binding Energy (BE) is the energy equivalent of the mass defect. It represents the energy required to completely separate the nucleons in a nucleus, or the energy released when nucleons combine to form a nucleus.
- 3Binding Energy per Nucleon (BE/A) is a key indicator of nuclear stability. Nuclei with higher BE/A are more stable. The BE/A curve peaks around A=56 (Iron), indicating maximum stability.
- 4Energy is released in nuclear reactions (fission or fusion) if the products have a higher binding energy per nucleon than the reactants, moving towards greater stability on the BE/A curve.
- 5When using atomic masses instead of nuclear masses, ensure correct handling of electron masses in the mass defect calculation. Typically, if atomic masses are used, it simplifies to Δm = [Z * m_H + (A - Z) * m_n] - M_atom (where m_H is mass of a hydrogen atom and M_atom is mass of the atom).
⚠️ Common Mistakes
- ✕Incorrectly calculating mass defect, especially by confusing atomic masses with nuclear masses or making algebraic errors in subtraction.
- ✕Failing to convert units properly, e.g., using mass in kg with 931.5 MeV/c^2 or incorrect application of c^2.
- ✕Misinterpreting the Binding Energy per Nucleon curve, leading to incorrect predictions about energy release in fission vs. fusion.
📝 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