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A radio isotope 'X' with a half-life 1.4 × 10⁹ years decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio 1:7. The age of the rock is:

1. 1.96 × 10⁹ years
2. 3.92 × 10⁹ years
3. 4.20 × 10⁹ years
4. 8.40 × 10⁹ years

Correct answer: 3.92 × 10⁹ years

Solution

The ratio of 'X' to 'Y' being 1:7 implies that 1 part of 'X' remains while 7 parts have decayed. This means 1/8 of the original 'X' remains. Using the formula N/N₀ = (1/2)^(t/T), where N/N₀ = 1/8 and T = 1.4 × 10⁹ years, we solve for t to get t = 3.92 × 10⁹ years.

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