Question

A fresh radioactive sample is given at t=0 its decay fraction are 1/5 at t1 instant and 4/5 at t2 instant it’s mean life is
a)t2-t1/ln2
b)t2-t1/2
c)t2-t1/ln4
d)t2-t1/4

Answer 1

The mean life is 1/ λ = t2 - t1 / ln 4

Option (C) is correct.

Explanation:

Decay fraction at t1:

At t = t1    N / No = 1/5

Decay fraction at t2:

At t2 =     N / No = 4/5

1/5 = e^-λt1   -----(1)

4/5 = e^-λ/t2   -------(2)

Now dividing equation 2 by 1.

1 / 4   = e^-λ/t1 / e^-λ/t2

4 = e^λ ( t2 - t1)

ln 4 = ln e^λ ( t2 - t1)

ln 4 = λ ( t2 - t1 )

Mean life =  1/ λ = t2 - t1 / ln 4

Thus the mean life is 1/ λ = t2 - t1 / ln 4