A radioactive sample is undergoing α decay. At any time t1, its activity is A and another time t2 , the activity is A5 . What is the average life time for the sample?
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a
t2−t1ln 5
b
ln 5t2−t1
c
t1−t2ln 5
d
ln(t2+t1)2
answer is A.
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Detailed Solution
Activity, A=A0e−λt At time t=t1,A=A0e−λt1 At time t=t2,A5=A0e−λt2 Dividing, 5=eλt2−t1⇒ln5=λt2−t1⇒λ=ln5t2−t1 Now, average life =T=1λ=t2−t1ln5