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A radioactive sample is undergoing $α$ decay. At any time $t_{1}$ , its activity is A and another time $t_{2}$ , the activity is $\frac{A}{5}$ . What is the average life time for the sample?

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t2−t1ln 5

ln 5t2−t1

t1−t2ln 5

ln(t2+t1)2

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detailed solution

Correct option is A

Activity, A=A0e−λt At time t=t1,A=A0e−λt1 At time t=t2,A5=A0e−λt2 Dividing, 5=eλt2−t1⇒ln⁡5=λt2−t1⇒λ=ln⁡5t2−t1 Now, average life =T=1λ=t2−t1ln⁡5

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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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Ready to Test Your Skills?

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A radioactive sample is undergoing $α$ decay. At any time $t_{1}$ , its activity is A and another time $t_{2}$ , the activity is $\frac{A}{5}$ . What is the average life time for the sample?