Nuclear Physics And Radioactivity Question 370
Question: The activity of a sample of a radioactive material is A, at time $ t_{1} $ and $ A_{2} $ at time $ t_{2} $ $ (t_{2}>t_{1}). $ If its mean life T, then [BHU 2002]
Options:
A) $ A_{1}t_{1}=A_{2}t_{2} $
B) $ A_{1}-A_{2}=t_{2}-t_{1} $
C) $ A_{2}=A_{1}{{e}^{(t_{1}-t_{2})/T}} $
D) $ A_{2}=A_{1}{{e}^{(t_{1}/t_{2})T}} $
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Answer:
Correct Answer: C
Solution:
$ A=A_{0}{{e}^{-\lambda t}}=A_{0}{{e}^{-t/\tau }}; $ where $ \tau = $ mean life So
$ \Rightarrow \Delta L=\frac{h}{2\pi }(n_{2}-n_{1}) $
Þ $ A_{0}=\frac{A_{1}}{{{e}^{-t_{1}/T}}}=A_{1}{{e}^{t_{1}/T}} $
$ \therefore A_{2}=A_{0}{{e}^{-t/T}}=(A_{1}{{e}^{t_{1}/T}}),{{e}^{-t_{2}/T}}\Rightarrow A_{2}=A_{1}{{e}^{(t_{1}-t_{2})/T}} $
BETA
