A sample of rock from the moon was found to contain the elements X and Y in 1:7 ratio by mole. Element is radioactive it decays to Y with half life of `6.93 xx 10^(9)` years
`X to Y`
`t_(1//2) = 6.93 xx 10^(9)` yrs
What is the age of the rock?

Options

A. `2.079 xx 10^(10)` yrs
B. `1.33 xx 10^(9)` years
C. `1.94 xx 10^(10)` years
D. `10^(10)` years

Answer

a

Explanation

`N_(0) = 1 + 7 = 8` (initial mole of X
N = 1 (Remaining mole of X)
We know,
`(0.693)/(t_(1//2)) = (2.303)/(t) log ((N_(0))/(N))`
`(0.693)/(6.93 xx 10^(9)) = (2.303)/(t) log (8)/(1)`
`t = 2.079 xx 10^(10)` years