The final product of `U^(238)` is `Pb^(206)`. A sample of pitchblende contains `0.0453 g` of `Pb^(206)` for every gram of `U^(238)` present in it. Supposing that the mineral pitchblende formed at the time of formation of the earth did not contain any `Pb^(206)`, calculate the age of the earth (half-life period of `U^(238) = 4.5 xx 10^(9)` years).

Explanation

To calculate the age of the Earth based on the decay of uranium-238 to lead-206, we can follow these steps:

### Step 1: Understand the relationship between uranium-238 and lead-206
The decay of uranium-238 (U-238) leads to the formation of lead-206 (Pb-206). In the given problem, we know that for every gram of U-238, there is 0.0453 grams of Pb-206 present.

### Step 2: Determine the initial amount of uranium-238
Let’s assume we have 1 gram of U-238 currently. Since Pb-206 was not present when the Earth formed, the initial amount of U-238 would be the current amount plus the amount that has decayed into Pb-206.

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