In a sample of pitchblende the ratio of `""^(206)Pb, ""^(238)U= 0.2: 1` by weight. If the disintegration constant of `""^(238)U " is " 1.54 xx 10^(-10)` per year and all Pb is supposed to be originated from uranium, what will be the age of the mineral?

Explanation

To solve the problem of determining the age of the mineral pitchblende based on the given ratio of lead-206 (Pb-206) to uranium-238 (U-238), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Ratio**:
The ratio of Pb-206 to U-238 by weight is given as 0.2:1. This means for every 1 part of U-238, there are 0.2 parts of Pb-206.

2. **Convert the Ratio to a Fraction**:
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