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QPages 442-444: Q31: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q31 Solution: A point source emitting alpha particles is placed at a distance …
A point source emitting alpha particles is placed at a distance of 1 m from a counter which records any alpha particle falling on its window. If the source contains active nuclei and the counter records a rate of 50000 counts/second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.
Step-by-Step Verified Solution
**Answer:** Decay constant _ = 1.05 _ 10__ s__.
**Step-by-Step Explanation:**
Given: N = 6.0 _ 10__ active nuclei, distance d = 1 m, window area A = 1 cm_ = 10__ m_, count rate = 50000/s.
Solid angle subtended by window: � = A/(4�d_) = 10__/(4� _ 1_) = 7.96 _ 10__.
Total emission rate = count rate / � = 50000 / 7.96 _ 10__ = 6.28 _ 10_ /s.
Activity A = _N _ _ = A/N = 6.28 _ 10_ / 6.0 _ 10__ = 1.05 _ 10__ s__.
Standard: 1.05 _ 10__ s__ (checking calculation)[citation:2].
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