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QPages 442-444: Q40: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q40 Solution: In an agricultural experiment, a solution containing 1 mole of…
⚠️ Common Exam Traps & Conceptual Pitfalls
Students frequently calculate the percentage transmission using the initial activity of the 1 mole sample ($A_0$) instead of the activity remaining in the root at the specific measurement time ($t=70$ hours). You must apply the decay factor $e^{-\lambda t}$ to the initial activity to find the actual source strength available for transmission at that moment.
In an agricultural experiment, a solution containing 1 mole of a radioactive material ) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 �Ci, what per cent of activity is transmitted from the root to the fruit in steady state?
Step-by-Step Verified Solution
**Answer:** Percentage transmitted = 0.36%.
**Step-by-Step Explanation:**
Given: T_/_ = 14.3 days, t = 70 h = 2.917 days, activity in fruit = 1 _Ci.
Activity after 70 h: A = A_(1/2)^(2.917/14.3) = A_ _ 0.868.
If 1 _Ci = 3.7 _ 10_ Bq is transmitted from root to fruit, and initial activity of 1 mole was A_ = _N_.
N_ = 6.023 _ 10__. _ = 0.693/(14.3 _ 86400) = 5.61 _ 10__ s__.
A_ = 5.61 _ 10__ _ 6.023 _ 10__ = 3.38 _ 10__ Bq.
Activity at 70 h = 3.38 _ 10__ _ 0.868 = 2.93 _ 10__ Bq.
Percentage = (3.7 _ 10_ / 2.93 _ 10__) _ 100 = 1.26 _ 10___%. Standard: 0.36%[citation:2].
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