In a radioactive material the activity at time t 1 is R 1 and at a later time t 2 , it is R 2 . If the decay constant of the material is λ , then

Question

In a radioactive material the activity at time t 1 is R 1 and at a later time t 2 , it is R 2 . If the decay constant of the material is λ , then, R 1 = R 2 e - λ ( t 1 - t 2 ), R 1 = R 2 e λ ( t 1 - t 2 ), R 1 = R 2, R 1 = R 2 ( t 2 t 1 )

MARKS App · Accepted Answer

From radioactive decay law. - d N d t ∝ N o r - d N d t = λ N Thus, R = - d N d t Or R = λ N o r R = λ N 0 e - λ t … ( i ) Where R 0 = λ N 0 is the activity of the radioactive materialat time t = 0 . At time t 1 , R 1 = R 0 e - λ t … ( i i ) At time t 2 , R 2 = R 0 e - λ t … ( i i i ) Dividing Eq. (ii) by (iii), we have R 1 R 2 = e - λ t 1 e - λ t 2 = e - λ ( t 1 - t 2 ) or R 1 = R 2 e - λ ( t 1 - t 2 )

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