Rankers Physics

Nucleus: Practice Problem & Solution

A radio isotope $X$ with a half life of $1.4 \times 10^9$ 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: (2014)
$1.96 \times 10^9$ years
$3.92 \times 10^9$ years
$4.20 \times 10^9$ years
$8.40 \times 10^9$ years

Solution Explained:

To solve this problem, we apply the core principles of Nucleus. Understanding the underlying formula is key to arriving at the correct answer below:

Ratio $X/Y = 1/7$ implies $X/(X+Y) = 1/8 = (1/2)^3$. Thus, 3 half-lives have elapsed. The age of the rock is $3 \times 1.4 \times 10^9 = 4.2 \times 10^9$ years.

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