The variation of decay rate of two radioactive samples A and B with time is shown in fig.

Which of the following statements are true?

Options

A. Decay constant of `A` is greater than that of `B`, hence `A` always decays faster than `B`.
B. Decay constant of `B` is greater than that of `A` but its decay rate is always smaller than that of `A`.
C. Decay constant of `A` is greater than that of `B` but it does not always decay faster then `B`.
D. Decay constant of `B` is smaller than that of `A` at a later instant.

Answer

C, D

Explanation

`|(dN)/(dt)| = lambda N_(0)e^(-lambdat) rArr |(d^(2)N)/(dt^(2))| = lambda^(2) N_(0^(e^(lambdat)))`
at instant when
`|(dN)/(dt)|_(A) = |(dN)/(dt)|_(B), ("slope")_(A) gt ("slope")_(B)`
`rArr lambda_(A) gt lambda_(B)`.