In a sample initially there are equal number of atoms of two radioactive isotopes A and B. 3 days later the number of atoms of A is twice that of B. Half life of B is `1.5` days. What is half life of isotope A? (in days)

Answer

`0003`

Explanation

`A B t=0 N_(0) N_(0)`
`t_(0)=3 days 2N N`
`2N=N_(0)(0.5)t_(0)//tau_(1)`
`N=N_(0)(0.5) t_(0)//tau_(2)`
`2=(0.5) t_(0)(1/tau_(1)-1/tau_(2))`
`Rightarrow 0.5^(-1)=(0.5)(3/tau_(1)-2)`
`Rightarrow -1=3/tau_(1)-2 :.tau_(1)=3` days