`._(238)^(92)U` by sucessive radioactive decays changes to `._(82)^(206) Pb`. A sample of uranium ore was analysed and found to contain `1.0g^(238)U` and `0.1g^(206)Pb`. Assuming that `.^(206)Pb` has accumlated due to delay of uranium, find out the age of ore.
(`t_(1//2)` for `.^(238)U = 10^(9)` year)

Explanation

To determine the age of the uranium ore, we will follow these steps:

### Step 1: Understand the decay process
Uranium-238 decays into Lead-206 through a series of radioactive decays. We are given that the sample contains 1.0 g of Uranium-238 and 0.1 g of Lead-206. We need to assume that all the Lead-206 present has originated from the decay of Uranium-238.

### Step 2: Calculate the number of moles of Uranium-238 and Lead-206
1. **Calculate moles of Uranium-238**:
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