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 than B
D. Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant

Answer

c,d

Explanation

From the given , figure it is clear that slope of curve A is greater than that of curve B. So rate of decay is faster for A than that of B.

We know that `((dN)/(dt)) prop , lambda` at any instant of time hence we can say that `lambda_(A) gt lambda_(B)` At point P shown in the diagram the two curve intersect.
Hence at point p rate of decay for both A and B is the same.