A source contains two phosphorus radionuclides `._(15)P^(35) (T_(1//2)=14.3"days")` and `._(15)P^(33) (T_(1//2)=25.3"days")`. Initially, `10%` of the decays come from `._(15)P^(35)`. How long one must wait until `90%` do so?

Explanation

To solve the problem, we need to find the time \( T \) required for the decays from the phosphorus radionuclide \( _{15}P^{35} \) to constitute 90% of the total decays, given that initially 10% of the decays come from \( _{15}P^{35} \) and 90% from \( _{15}P^{33} \).

### Step-by-Step Solution:

1. **Define Initial Conditions:**
Let the initial number of nuclei of \( _{15}P^{35} \) be \( X \) and the initial number of nuclei of \( _{15}P^{33} \) be \( 9X \) (since 10% comes from \( _{15}P^{35} \) and 90% from \( _{15}P^{33} \)).

2. **Decay Formulas:**
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