Half-life of `""^(210)Pb` is 22 years. 2gram of lead is allowed decay for 11 years. (a) How much lead is left ?and (b) What is the percentage decay ?

Explanation

Number of half - lives (n) `= ("Total time")/("Half - life") = (11y)/(22y) = (1)/(2) = 0.5`
(a) Amount of lead left undecayed `= ("Amount of lead taken")/(2^(n)) = (2)/(sqrt(2)) = 1.414 g`
(b) Amount of lead decayed = Amount taken - left amount
` = 2-1.414 = 0.586 g`
Percentage of lead decayed ` = (0.586 xx 100)/(2) = 29.3%`