Question

A radio isotope X with a half life $1.4\times {10}^9$ 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

• A. $1.96\times {10}^{9}years$
• B. $3.92\times {10}^{9}years$
• C. $4.20\times {10}^{9}years$
• D. $8.40\times {10}^{9}years$

Answer 1

The correct option is C $4.20\times {10}^{9}years$

X : Y = 1 : 7
X : (X + Y) = 1 : 8 = 1 : 23
$\Rightarrow$ 3 half life
$\therefore \Delta T=3\times 1.4\times {10}^{9}yrs=4.2\times {10}^{9}yrs$.