Verified Solution • 2025–26 Session moderate

QPages 442-444: Q22: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q22 Solution: The decay constant of is . a) What is the average-life of ? b)…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the average life ($\tau = 1/\lambda$) with the half-life ($T_{1/2} = \ln 2 / \lambda$), leading to a factor of $\ln 2 \approx 0.693$ error. Always verify if the question asks for mean lifetime or half-life, as they differ by a constant factor.

The decay constant of 238U^{238}\text{U} is 4.9×10−18 s−14.9 \times 10^{-18} \text{ s}^{-1}. a) What is the average-life of 238U^{238}\text{U}? b) What is the half-life of 238U^{238}\text{U}? c) By what factor does the activity of a 238U^{238}\text{U} sample decrease in 9×1099 \times 10^9 years?

Step-by-Step Verified Solution

**Answer:** (a) Average-life = 6.47 _ 10_ years (b) Half-life = 4.5 _ 10_ years (c) Activity decreases by a factor of 4. **Step-by-Step Explanation:** Given: _ = 4.9 _ 10___ s__. (a) _ = 1/_ = 1/(4.9 _ 10___) = 2.04 _ 10__ s = 6.47 _ 10_ years. (b) T_/_ = 0.693/_ = 0.693/(4.9 _ 10___) = 1.41 _ 10__ s = 4.5 _ 10_ years. (c) t = 9 _ 10_ years = 2 T_/_. Activity factor = (1/2)_ = 0.25, so it decreases by a factor of 4[citation:9].

All Questions in this Chapter

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