In the chemical analysis of a rock the mass ratio of two radioactive isotopes is found to be `100:1`. The mean lives of the two isotopes are `4xx10^9` years and `2xx10^9` years, respectively. If it is assumed that at the time of formation the atoms of both the isotopes were in equal propotional, calculate the age of the rock. Ratio of the atomic weights of the two isotopes is `1.02:1`.

Explanation

To solve the problem, we need to calculate the age of the rock based on the given mass ratio of two radioactive isotopes, their mean lives, and the assumption that they were formed in equal proportions. Here’s the step-by-step solution:

### Step 1: Understand the Given Data
- Mass ratio of isotopes \( M_1 : M_2 = 100 : 1 \)
- Mean lives of isotopes:
- Isotope 1: \( \tau_1 = 4 \times 10^9 \) years
- Isotope 2: \( \tau_2 = 2 \times 10^9 \) years
- Atomic weight ratio \( A_1 : A_2 = 1.02 : 1 \)
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