The half life of `.^(212)Pb` is 10.6 hour. It undergoes decay to its daughter (unstable) element `.^(212)Bi` of half life 60.5 minute. Calculate the time at which the daughter element will have maximum activity.

Explanation

`lambda_(Pb) = (0.693)/(10.6 xx 60) = 1.0896 xx 10^(-3) "min"^(-1)`
`lambda_(Bi) = (0.693)/(60.5) = 11.45 xx 10^(-3) "min"^(-1)`
`t_("max") = (2.303)/(lambda_(Bi) - lambda_(Pb)) log (lambda_(Bi))/(lambda_(Pb))`
`= (2.303)/((11.45 xx 10^(-3) - 1.0896 xx 10^(-3))) xx log, (11.45 xx 10^(-3))/(1.0896 xx 10^(-3))`