Question

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 75% of the lead to decay? (Round your answer to two decimal places.)

Answer 1

It will take 6.6 hours for 75% of the lead to decay.

Step-by-step explanation:

The radioactive decay follows first order rate law

The half life and rate constant are related as

`k=rate constant=(0.693)/(halflife)=(0.693)/(3.3)=0.21h^(-1)`

The rate law for first order reaction is

`time=(1)/(k)(ln[(A_(0))/(A_(t))]`

Where

A0 = initial concentration = 1 g

At= final concentration = 0.25 g (as 75% undergoes decay so 25% left]

`time=(1)/(0.21)(ln((1)/(0.25))=6.6hours`