A radioactive substance `"A"` having `N_(0)` active nuclei at `t=0`, decays to another radioactive substance `"B"` with decay constant `lambda_(1)`. `B` further decays to a stable substance `"C"` with decay constant `lambda_(2)`. (a) Find the number of nuclei of `A, B` and `C` time `t`. (b) What should be the answer of part (a) if `lambda_(1) gt gt lambda_(2)` and `lambda_(1) lt lt lambda_(2)`

Explanation

To solve the problem step by step, we will analyze the decay processes of the radioactive substances A, B, and C.

### Part (a): Finding the number of nuclei of A, B, and C at time t

1. **Decay of substance A**:
- The decay of substance A can be described by the differential equation:
\[
-\frac{dN_A}{dt} = \lambda_1 N_A
...