Radioactivity — Alpha, beta, gamma decay
Nuclei
7
JEE Qs
8%
Hard
75
min
Master the conservation laws (A, Z, momentum, energy) and Q-value calculations for each decay type, paying close attention to mass accounting for emitted particles and recoil.
🧮 Key Formulas
✅ Key Points for JEE
- 1In all radioactive decay processes, the total mass number (A), atomic number (Z), total energy, linear momentum, and angular momentum are strictly conserved.
- 2Alpha decay involves the emission of an alpha particle (_2^4 He nucleus), decreasing the parent nucleus's A by 4 and Z by 2.
- 3Beta-minus decay (β-) involves a neutron transforming into a proton, emitting an electron and an antineutrino (ν̄); Z increases by 1, A remains unchanged. Beta-plus decay (β+) involves a proton transforming into a neutron, emitting a positron and a neutrino (ν); Z decreases by 1, A remains unchanged.
- 4Gamma decay occurs when an excited nucleus transitions to a lower energy state, emitting a high-energy photon (gamma ray). A and Z remain unchanged, and it often follows alpha or beta decay.
- 5The energy spectrum of alpha particles and gamma rays is discrete (monoenergetic), while the energy spectrum of electrons/positrons in beta decay is continuous because the energy released is shared between the beta particle and the accompanying neutrino/antineutrino.
- 6The Q-value represents the total energy released during decay, which appears as kinetic energy of the decay products and sometimes as gamma radiation. For beta decay, care must be taken with electron masses when using atomic mass units in Q-value calculations.
⚠️ Common Mistakes
- ✕Incorrectly balancing mass number (A) and atomic number (Z) in decay equations, especially confusing the change in Z for beta-minus versus beta-plus decay.
- ✕Forgetting to include the antineutrino (ν̄) in beta-minus decay or the neutrino (ν) in beta-plus decay, or not understanding their role in energy sharing.
- ✕Incorrectly calculating the Q-value for beta decay by not properly accounting for the mass of emitted electrons/positrons, especially when using atomic masses.
- ✕Assuming that the kinetic energy of the emitted alpha particle or beta particle is always equal to the total Q-value, thereby neglecting the recoil kinetic energy of the daughter nucleus.
📝 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