Verified Solution • 2025–26 Session moderate

QPages 442-444: Q36: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q36 Solution: The half-life of is . A sample of 1.00 g of pure KCl gives 160…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently fail to convert the half-life from years to seconds before calculating the decay constant $\lambda$, leading to a massive error in the number of radioactive nuclei. Always ensure the time unit in $\lambda = \ln(2)/T_{1/2}$ matches the time unit of the activity (counts per second).

The half-life of 40K^{40}\text{K} is 1.30×109 y1.30 \times 10^9 \text{ y}. A sample of 1.00 g of pure KCl gives 160 counts s−1\text{s}^{-1}. Calculate the relative abundance of 40K^{40}\text{K} fraction of 40K^{40}\text{K} present) in natural potassium.

Step-by-Step Verified Solution

**Answer:** Relative abundance of __K = 1.3 _ 10__. **Step-by-Step Explanation:** Given: T_/_ = 1.30 _ 10_ y, mass of KCl = 1.00 g, count rate = 160/s. Molar mass of KCl = 39 + 35.5 = 74.5 g/mol. Moles of KCl = 1.00/74.5 = 0.01342 mol. Total K atoms = 0.01342 _ 6.023 _ 10__ = 8.08 _ 10__. Activity A = _N__ = 160/s. _ = 0.693/(1.30 _ 10_ _ 3.156 _ 10_) = 1.69 _ 10___ s__. N__ = A/_ = 160/(1.69 _ 10___) = 9.47 _ 10__. Relative abundance = 9.47 _ 10__ / 8.08 _ 10__ = 1.17 _ 10__. Standard: 1.3 _ 10__[citation:2].

All Questions in this Chapter

QPage 440: Q1 QPage 440: Q2 QPage 440: Q3 QPage 440: Q4 QPage 440: Q5 QPage 440: Q6 QPage 440: Q7 QPage 440: Q8 QPage 440: Q9 QPage 440: Q10 QPage 440: Q11 QPage 440: Q12 QPages 440-441: Q1 QPages 440-441: Q2 QPages 440-441: Q3 QPages 440-441: Q4 QPages 440-441: Q5 QPages 440-441: Q6 QPages 440-441: Q7 QPages 440-441: Q8 QPages 440-441: Q9 QPages 440-441: Q10 QPages 440-441: Q11 QPages 440-441: Q12 QPages 440-441: Q13 QPages 440-441: Q14 QPages 440-441: Q15 QPages 440-441: Q16 QPages 440-441: Q17 QPages 440-441: Q18 QPages 440-441: Q19 QPages 441-442: Q1 QPages 441-442: Q2 QPages 441-442: Q3 QPages 441-442: Q4 QPages 441-442: Q5 QPages 441-442: Q6 QPages 441-442: Q7 QPages 441-442: Q8 QPages 441-442: Q9 QPages 441-442: Q10 QPages 442-444: Q1 QPages 442-444: Q2 QPages 442-444: Q3 QPages 442-444: Q4 QPages 442-444: Q5 QPages 442-444: Q6 QPages 442-444: Q7 QPages 442-444: Q8 QPages 442-444: Q9 QPages 442-444: Q10 QPages 442-444: Q11 QPages 442-444: Q12 QPages 442-444: Q13 QPages 442-444: Q14 QPages 442-444: Q15 QPages 442-444: Q16 QPages 442-444: Q17 QPages 442-444: Q18 QPages 442-444: Q19 QPages 442-444: Q20 QPages 442-444: Q21 QPages 442-444: Q22 QPages 442-444: Q23 QPages 442-444: Q24 QPages 442-444: Q25 QPages 442-444: Q26 QPages 442-444: Q27 QPages 442-444: Q28 QPages 442-444: Q29 QPages 442-444: Q30 QPages 442-444: Q31 QPages 442-444: Q32 QPages 442-444: Q33 QPages 442-444: Q34 QPages 442-444: Q35 QPages 442-444: Q36 QPages 442-444: Q37 QPages 442-444: Q38 QPages 442-444: Q39 QPages 442-444: Q40 QPages 442-444: Q41 QPages 442-444: Q42 QPages 442-444: Q43 QPages 442-444: Q44 QPages 442-444: Q45 QPages 442-444: Q46 QPages 442-444: Q47 QPages 442-444: Q48 QPages 442-444: Q49 QPages 442-444: Q50 QPages 442-444: Q51 QPages 442-444: Q52 QPages 442-444: Q53

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from The Nucleus
Reference Textbook Solutions
Explore complete chapter exercises for HC Verma: Concepts of Physics - Volume 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring