Half Life + Radioactive Decay
Nuclei
40
JEE Qs
8%
Hard
75
min
Master the interconversion between decay constant, half-life, and mean life, and practice problems differentiating between the amount remaining versus decayed.
🧮 Key Formulas
✅ Key Points for JEE
- 1Radioactive decay is a random, exponential process where the rate of decay is proportional to the number of undecayed nuclei present.
- 2The decay constant (λ), half-life (T₁/₂), and mean life (τ) are intrinsic properties of a radionuclide and are independent of external physical or chemical conditions.
- 3Activity (A) is the rate of decay (disintegrations per second) and is directly proportional to the number of radioactive nuclei (N) at that instant (A = λN).
- 4Half-life (T₁/₂) is the time required for half of the initial radioactive nuclei to decay, while mean life (τ) is the average lifetime of a radioactive nucleus.
- 5For problems involving integer multiples of half-lives, using the formula N = N₀ * (1/2)^(t / T₁/₂) is often quicker and less prone to calculation errors than the exponential form.
⚠️ Common Mistakes
- ✕Confusing half-life (T₁/₂) with mean life (τ) or incorrectly interchanging their formulas in calculations.
- ✕Errors in logarithmic and exponential calculations, especially regarding the base (e vs 10) or incorrect application of log properties.
- ✕Mixing up the 'number/fraction of nuclei remaining' with the 'number/fraction of nuclei decayed' during problem solving.
- ✕Assuming that the decay constant or half-life can be affected by external factors like temperature, pressure, or chemical state.
📝 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