Verified Solution • 2025–26 Session
moderate
QPages 442-444: Q19: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q19 Solution: The decay constant of electron capture to ) is . a) What is the …
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently confuse the fraction of nuclei that have decayed with the fraction remaining, leading to the incorrect substitution of $N/N_0 = 0.25$ instead of $0.75$ in the exponential decay law. Always verify that the ratio $N/N_0$ represents the undecayed population, which is calculated as $1 - \text{fraction decayed}$.
The decay constant of electron capture to ) is . a) What is the half-life? b) What is the average-life? c) How much time will it take to convert 25% of this isotope of mercury into gold?
Step-by-Step Verified Solution
**Answer:** (a) Half-life = 1.07 h (b) Average-life = 1.54 h (c) Time = 0.445 h.
**Step-by-Step Explanation:**
Given: _ = 1.8 _ 10__ s__.
(a) T_/_ = 0.693/_ = 0.693/(1.8 _ 10__) = 3850 s = 1.07 h.
(b) _ = 1/_ = 1/(1.8 _ 10__) = 5556 s = 1.54 h.
(c) 25% converted means N/N_ = 0.75. N = N_e^(-_t).
0.75 = e^(-_t) _ t = -ln(0.75)/_ = 0.2877/(1.8 _ 10__) = 1598 s = 0.444 h[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