A radio isotope `X` with a half-life `1.4 xx 10^9` years decays of `Y` which is stable. A sample of the rock from a cave was found to contain `X` and `Y` in the ratio `1 : 7`. The age of the rock is.

Answer

B

Explanation

`{:(8x,0,t=0),(Xrarr,Y("stable"),),(x,7x,t=t):}`
for `X, N_(0) = 8x, N = x`
`(N)/(N_(0)) = ((1)/(2))^(n) rArr (x)/(8x) = ((1)/(2))^(n)`
`n = 3`
`t = nT_(1)//2 =3xx1.4 xx 10^(9) = 4.2 xx 10^(9) years`