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QPages 442-444: Q21: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q21 Solution: Radioactive has a half-life of 8.0 days. A sample containing…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently treat the decay constant as a variable and try to recalculate it at t=4 days; however λ = ln 2 / T½ is a fixed property of the isotope and does not depend on how long the sample has decayed.

Radioactive 131I^{131}\text{I} has a half-life of 8.0 days. A sample containing 131I^{131}\text{I} has activity 20 �Ci at t = 0. a) What is its activity at t = 4 days? b) What is its decay constant at t = 4.0 days?

Step-by-Step Verified Solution

**Answer:** (a) Activity at t = 4 days = 14.1 _Ci (b) Decay constant remains the same. **Step-by-Step Explanation:** (a) T_/_ = 8 days. A = A_ (1/2)^(t/T_/_) = 20 _ (1/2)^(4/8) = 20 _ 0.707 = 14.1 _Ci. (b) The decay constant _ is a fundamental property of the isotope and does not change with time. _ = 0.693/8 = 0.0866 day__[citation:2].

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