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

Radioactive decay follows first order kinetics. 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
`2-1414=0.586g`
The percentage of lead decayed
`=(0.586xx100)/(2)=29.3%`