Question

A radioactive sample is undergoing alpha decay .At any time t1,its activity is A and another time t2,the activity is A/5.What is the average life time for the sample?

Answer 1

Answer:

avg. life = 1/λ = (t2 – t1)/ ln(5)

Explanation:

For activity of radioactive sample :

A =  A 0e − λ t 1  ….(1)

A/5 =  A 0 e − λ t 2  ….(2)  

From (1)/(2)

5 =  e − λ ( t 1 − t 2 )

ln (5) = (t2 – t1) λ

⇒ λ = ln(5)/t2 – t1

avg. life = 1/λ = (t2 – t1)/ ln(5)