In moon rock sample the ratio of the number of stable argon-40 atoms present to the number of radioactive potassium-40 atoms is 7:1. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of 2.5×109 yr. The age of the rock is

Let the number of radioactive Potassium atoms present initially (t=0) is N0 and the number of stable argon atoms at t=0 is zero. After time t the number of stable argon atoms is m and the radioactive potassium atoms is N0 - m give that N0−mm=17, m=78N0 and N0−m=18N0 since after one half-life N0 reduces to N0 / 2 after 2 half-lives N0 / 4 and after 3 half-lives it reduces to N0 /8 t=nT=3×2.5×109 years Thus, = 7.5 × 109 year