A mixture of `""^(239)Pu and ""^(240)Pu` has a specific activity of `6.0xx 10^(9)` dis/s. The half-lives of the isotopes are `2.44 xx 10^(4) and 6.58 xx 10^(3) `years, respectively. Calculate the isotopic composition of this sample

Explanation

To solve the problem of determining the isotopic composition of a mixture of plutonium isotopes \(^{239}\text{Pu}\) and \(^{240}\text{Pu}\), we need to follow these steps:

### Step 1: Define Variables
Let:
- \( a \) = fraction of \(^{239}\text{Pu}\)
- \( b \) = fraction of \(^{240}\text{Pu}\)

From the problem, we know that:
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