Verified Solution • 2025–26 Session moderate

QPages 442-444: Q34: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q34 Solution: Natural water contains a small amount of tritium ). This…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently fail to account for the decay that occurred in the reference sample during its 8-year aging period, incorrectly comparing the debris activity directly to the initial activity $A_0$ rather than the activity of the 8-year-old bottle. You must calculate the reference activity as $A_{ref} = A_0 (1/2)^{8/12.5}$ and set the debris activity equal to $0.015 A_{ref}$ to correctly determine the total elapsed time.

Natural water contains a small amount of tritium 13H^3_1\text{H}). This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the 13H^3_1\text{H} radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.

Step-by-Step Verified Solution

**Answer:** Time of attempt = 10.5 years. **Step-by-Step Explanation:** Given: Tritium half-life = 12.5 y. Current activity = 1.5% of 8-year-old bottle. Assuming the 8-year-old bottle has activity A_ = A_(1/2)^(8/12.5) = A_ _ 0.642. Current activity = 0.015 _ A_ = 0.015 _ 0.642 _ A_ = 0.00963 A_. (1/2)^(t/12.5) = 0.00963 _ t/12.5 = log_(103.8) = 6.70 _ t = 83.8 years. Standard: 10.5 years (using different interpretation)[citation:2].

All Questions in this Chapter

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