How much time is taken by a radioactive sample to decay `(7//8)^(th)` of the initial quantity, if ts half-life is 12 days?

Options

A. 36 days
B. 12 days
C. 4 days
D. 24 days

Answer

A

Explanation

hald life `(t _(1//2)) =12` days
Let the total undecayed amount be `N _(0).`
Decayed amount `= ( 7 N _(0))/(8)`
Remain undecayed
`(N) = N _(0) - ( 7 N _(0))/(8) = ( N _(0))/(8)`
`N = ( N _(0))/(2 ^(n)) = (N _(0))/(8)`
`n = 3`
`nto` number of half life
`T = n xx t _(1//2) = 3 xx 12 = 36` days