In a sample of pitchblende the atomic ratio is `""^(206)Pb, ""^(238)U= 0.23: 1`. Calculate the age of the mineral, if half-life of uranium is taken as `4.5 xx 10^(9)` years. All lead originated from uranium.

Explanation

To calculate the age of the mineral sample based on the given atomic ratio of lead to uranium and the half-life of uranium, we can follow these steps:

### Step 1: Understand the relationship between lead and uranium
Given the atomic ratio of lead-206 (Pb) to uranium-238 (U) is 0.23:1, we can express this as:
\[ \frac{[Pb]}{[U]} = 0.23 \]
This means that for every 1 atom of uranium, there are 0.23 atoms of lead.
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