Question

A radioactive isotope `X` with a half-life of `1.37 xx 109` years decays to `Y` which is stable. A sample of rock from the moon was found to contain both the elements `X` and `Y` which were in the ratio of `1 : 7`. The age of the rock is.
A. `1.96xx10^(8)years`
B. `3.85xx10^(9)years`
C. `4.11xx10^(9)years`
D. `9.59xx10^(9)years`

Answer 1

Correct Answer - C
`{:(N_(0),0,t=0),(Xrarr,Y("stable"),),(N,N_(0)-N,t=t):}`
`(N)/(N_(0)-N) = (1)/(7) rArr 8N = N_(0)`
`(N)/(N_(0)) = (1)/(8)= ((1)/(2))^(3) = ((1)/(2))^(n) rArr n = 3`
`t = nT_(1//2) = 3xx1.37 xx 10^(9) = 4.11 xx 10^(9)` years