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

For `lambda_1 > > lambda_2`
`N_2 = (lambda_1N_0)/(-lambda_1)(-e^(-lambda_2t)) = N_0e^(-lambda_2t)`
For `lambda_1 < < lambda_2`
`N_2 = (lambda_1N_0)/(lambda_2)(e^(-lambda_1t)) = 0`.