A Radioactive element A says to B ''l am half of what you were when you are one fourth of what l was moreover l was `1.414` time than what you were '' If the half life of A is 8 days, what is the half life of 'B' is

Options

A. 4 days
B. 8 days
C. 16 days
D. 2 days

Answer

B

Explanation

Initial nuclides of X and `Y rArr X_(o)` and `Y_(o)`
After time 't' nuclides of X and `Y rArr X_(t)` and `Y_(t)`
`X_(t) = 1//2Y_(o), Y_(t) = 1//4X_(o)`
`X_(o) = 1.414Y_(o), Y_(t) = 1//4X_(o)`
Now, `X_(t) = X_(o)e^(-D_(1//t)) = 1//2Y_(o) , Y_(t) = Y_(o) e^(-D_(2//t)) = 1//4Y_(o)`
Dividing equation (i) by (ii) , we get
`X_(o) = sqrt2Y_(o) :. 2 = 2e^((D_(2) - D_(1)))t`
`:. e^(D_(2) - D_(1))t`
Q since t is not zero so `D_(2) = D_(1) rArr 8 "days"`.