A radio nuclide `A_(1)` with decay constant `lambda_(1)` transforms into a radio nuclide `A_2` with decay constant `lambda_(2)`. Assuming that at the initial moment, the preparation contained only the radio nuclide `A_(1)`
(a) Find the equation describing accumulation of radio nuclide `A_(2)` with time. (b) Find the time interval after which the activity of ratio nucliei `A_(2)` reaches its maximum value.

Options

A. `(ln(lambda_(2)//lambda_(1)))/(lambda_(2)-lambda_(1))`
B. `(ln(lambda_(1)//lambda_(2)))/(lambda_(1)-lambda_(2))`
C. `ln(lambda_(2)-lambda_(1))`
D. none of these

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Finding the equation describing the accumulation of radionuclide A2 with time.

1. **Understanding the Decay Process**:
- We have radionuclide A1 that decays into A2. The decay constant for A1 is \( \lambda_1 \) and for A2 is \( \lambda_2 \).
- Initially, at time \( t = 0 \), we have only A1, so \( N_{A1}(0) = N_0 \) (where \( N_0 \) is the initial quantity of A1).

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