Verified Solution • 2025–26 Session moderate

QPages 442-444: Q23: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q23 Solution: A certain sample of a radioactive material decays at the rate…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often plug the 50‑minute interval directly into $\lambda =-\ln(A/A_0)/t$ and report $\lambda$ in $\text{min}^{-1}$ while the problem expects $\text{s}^{-1}$, or they forget to convert the time when using the half‑life formula $T_{1/2}=0.693/\lambda$. Always keep the time units consistent: convert minutes to seconds before computing $\lambda$, then convert back if you need the half‑life in minutes.

A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. a) What is the decay constant of the sample? b) What is its half-life?

Step-by-Step Verified Solution

**Answer:** (a) _ = 3.05 _ 10__ s__ (b) Half-life = 38 min. **Step-by-Step Explanation:** Given: A_ = 500/s, A = 200/s, t = 50 min = 3000 s. A = A_e^(-_t) _ 200 = 500e^(-3000_). e^(-3000_) = 0.4 _ -3000_ = ln(0.4) = -0.916. _ = 3.05 _ 10__ s__. T_/_ = 0.693/_ = 0.693/(3.05 _ 10__) = 2272 s = 37.9 min � 38 min[citation:9].

All Questions in this Chapter

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