The correct option is A 4.11×109 years
Given that, T1/2=1.37×109 years
At present,
Number of K atomsNumber of Ar atoms=17
As there were no argon present initially, so
Number of K atoms present initially = number of K atoms + number of Ar atoms present now.
Let,
Number of K-atoms present nowNumber of K-atom present initially=NN0
⇒NN0=11+7=18
Let age of rock be n half-lives of K−nuclide. Then,
NN0=(12)n
⇒18=(12)n
⇒n=3
Therefore, the age of the rock is,
t=nT1/2
⇒t=3×1.37×109
⇒t=4.11×109 years
Hence, option (A) is correct.