The half life of `""^(212)Pb` is 10.6 hour, that of daughter `""^(212)Bi` is 60.5 min. How long will it take for a maximum daughter acitivity to grow in freshly separated `""^(212)Pb` ?

Options

A. 4.48 hr
B. 2.26 hr
C. 3.78 hr
D. 37 hr

Answer

C

Explanation

`lambda` for daughter `""^(212)Bi = (0.693)/(t_(0.5)) = 1.145 xx 10^(-2) min^(-1)`
`lambda` for present ` ""^(212)Pb = (0.693)/(10.6 xx 60) = 1.089 xx 10^(-3) min^(-1)`
As we known ` t_(max) = (2.303)/(lambda_(d) - lambda_(p)) log "" (lambda_(d))/(lambda_(p)) = (2.303)/(1.145 xx 10^(-2) - 1.089 xx 10^(-3))`
`log ""(lambda_(d))/(lambda_(p)) = (2.303)/(1.145 xx 10^(-2) - 1.089 xx 10^(-3))`