An isotope of Potassium `._(19)^(40) K ` has a half life of `1.4 xx 10^(9)`year and decays to Argon `._(18)^(40)Ar`which is stable.
(i) Write down the nuclear reaction representing this decay.
(ii) A sample of rock taken from the moon contains both potassium and argon in the ratio `1//3`. find age of rock

Answer

(i) `._(19)^(40) K rarr . _(18)^(40) Ar + ._(+1) beta ^(0) +v`

Explanation

(i) `._(19)^(40)Krarr._(18)^(40)Ar+.._(+1)" "^(0)e` (positron)
(ii) `t=(1)/(lambda) ln .(1)/((1//4))" " (K)/(Ar)=(1)/(3)` (Given ratio)
`=(1.4 xx10^(9))/(ln2) ln4 " " k=((1)/(4))`
`=2.8 xx 10^(9)` years