The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements ‘X’ and 'Y' were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

X→YInitial number of atoms,N0    0Number of atoms after time t N     N0−NAs per question NN0−N=177N=N0−N 8N=N0 NN0=18As NN0=12nwhere n is the no. of half lives∴   18=12n 123=12n ∴n=3 n=tT1/2  or   t=nT1/2=3×20years=60yearsHence, the age of rock is 60 years.