Initially two radioactive nucleus have same no of active nucleus their half life are 3 years and 4 years respectively after how many years, number of nucleus of one of the radioactive element is half the number of active nucleus of other radioactive element.

Explanation

To solve the problem, we need to find out after how many years the number of active nuclei of one radioactive element is half the number of active nuclei of the other radioactive element. We have two radioactive elements A and B with half-lives of 3 years and 4 years, respectively.

### Step-by-Step Solution:

1. **Define the Initial Conditions**:
Let the initial number of active nuclei for both elements A and B be \( N_0 \).

2. **Determine the Decay Constants**:
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