Question

A radioactive isotope x with half life of $1.37\times {10}^9$ years decays to y which is stable. A sample of rock from the moon was found to contain both the elements x and y in the ratio 1 : 7. What is the age of the rocks :

• A. $1.96\times {10}^8$ years
• B. $3.85\times {10}^9$ years
• C. $4.11\times {10}^9$ years
• D. $3.06\times {10}^9$ years

Answer 1

The correct option is C $4.11\times {10}^9$ years

Ratio of x:y = 1: 7

Active part of sample = x/x+y= 1/8

n=3

so it completes three half life so age of rock is $3t_{1/2}=3\ast 1.37\ast {10}^9=4.11\ast {10}^9$