At a given, t = 0, two radioactive substances A and B have equal activities. The ratio `(R_(B))/(R_(A))` of their activities after time t itself decays with time t as `e^(-3t)`, If the half-life of A is ln2, the half-life of B is :

Answer

4

Explanation

`lambda_(A)=N_(A)=lambda_(B)N_(B)" at "t=0`
After time t
`(R_(B))/(R_(A))=(lambda_(B)N_(B)e^(-lambda_(B)t))/(lambda_(A)N_(A)e^(-lambda_("At"))=e^((-lambda_(B)+lambda_(A))t`
`rArr" "lambda_(A)-lambda_(B)=-3," "(ln2)/(t_(1//2))-lambda_(B)=-3`
`lambda_(B)=(ln2)/(t_(1//2))+3," "lambda_(B)=4`
`rArr" "t_(1//2)=(4)/(ln2)" "rArr" "t_(1//2)=(ln2)/(4)`