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 70% of the lead to decay

4.62 hrs

Step-by-step explanation: there is 1g of pb-209 present and it's half life (time to reduce to it's half value) is 3.3 hours.

Half of the original value = 1g/2

= 0.5g

So

0.5g = 3.3 hrs

Now 70% of 1g is 0.7g

Value of pb-209 remaining at 70% removed is 1-0.7=0.3g

So the Time to decay to 0.3g is

=(0.7*3.3)/0.5

=2.31/0.5

= 4.62 hrs