Ncert Exercises & Solutions

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

Which of the following statements are true?

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

1. (a, b)

2. (a, c)

3. (b, d)

4. (c, d)

(4) Hint: Decay rate depends on the no. of nuclei in a sample.

Step 1: Find the decay rate of A and B from the graph.

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.

Step 2: Find the comparative decay constant for A and B.

We know that

(\frac{d N}{d t}) \propto

λ

at any instant of time hence we can say that

λ_{A}

λ_{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.