`'m_(1)'` g of non-radioactive isotopes `._(z)X^(A)` are mixed with `'M_(2)'` g of the radioactive isotopes `._(z)X^(A')`. How much will the specific activity decreases ? Half-life of `._(z)X^(A')=T` Take `N_(A)` as Avagardo number.

Answer

`((log_e 2)N_A m_(1))/(TA'(m_(1) +m_(2))`

Explanation

Before miximg the two, the specific activity `a_(1)` is given by
`a_(1)=(dN)/(d_(2)dt)=(lambdaN)/(m_(2))=(log_(3)2)/(T)xx(N_(A)m_(2))/(A')xx(N_(A)m_(2))/(A')xx(1)/(m_(2))`
`=(log_(e)2)/(T)xx(N_(A))/(A')`
After mixing, the activity `(a_2)` is given by
`a_(2)=(dN)/((m_(1)+m_(2))dt) =(log_(e)2)/(T)(N_(A)m_(2))/(A'(m_(1)+m_(2)))`
`:.` Change activity `=a_(1)-a_(1)=((log_(e)2)N_(A)m_(1))/(TA'(m_(1)+m_(2)))`.