The radioactivity of a given sample of whisky due to tritium (half life `12.3` years) was found to be only `3 %` of that measured in a recently purchased bottle marked `''7` years old''. The sample must have been prepared about.

Options

A. Before 70 years
B. Before 220 years
C. Before 420 years
D. Before 300 years

Answer

A

Explanation

We have `N_(1)=N_(0)e^(-lamda xx7)and N_(2)=N_(0)e^(-lamdax)`
`(N_(2))/(N_(1))=(3)/(100) = e^(lamda(7-x))or e^(lamda(x+7))=(100)/(3)`
`lamda(x-7)= "ln" (100)/(3)~~2.3 log_(10)2.3`
`"log"_(10)(100)/(3)=2.3 [2-0.4771]=2.3 xx1.5229`
But `lamda =(0.693)/(T_(1//2))=(0.693)/(12.5)`
`:. x-7=(12.5)/(0.693)xx2.3 xx1.5229`
`~~ (125)/(3)xx1.52 ~~ 63`
`:. xx =(63+7)` years = 70 years