Radioactivity (decay)

[sheepgomoo]

ok so im just starting physics units 1+2 and for holiday homework i was set some questions on radioactivity and decay.

So i understand the concepts... sort of. Basically theres unstable elements like uranium that eject alpha, beta and gamma particles to become more stable. And a half life is the time taken for half of the atoms in a radioactive sample to decay. i know the formula, its an exponential graph etc etc.

and then i come along this question:

212Bi83 decays into 212Po84 with a half life of one hour.
212Po84 decays into 208Pb82 with a half life of 3 x 10^-7 sec.
A pure sample of 212Bi83 of mass 8.0g is provided. What mass (in g) of the stable element 208Pb82 would there be after one hour?
A. 8.0 B. 4.0 C. 2.0 D. 1.0

By my general thinking it should be C, because its after two half lifes, but now im confused, because after an hour wouldnt the original sample of Bi decay into Po only? Or am i just reading into the question too much, because 3 x 10^-7 sec is really really fast, and them asking after one hour includes that less than one second.

am i even making sense? im getting more and more confused ;(

[dptjandra]

The one hour will include that 3 x 10^-7 seconds because it is so short.

So while the process is actually 212Bi83 --> 212Po84 --> 208Pb82, for the sake of answering the question, we can consider 212Bi83 --> 208Pb82.

The half life of 212Bi83 is one hour, so after one hour, we would expect there to be 4.0g of 212Bi83 and 4.0g of 208Pb82.

[echenzi]

Hmm in the one hour time frame, 4g of the Bi-212 would have decayed into Po-212. That can definitely be stated.

Given the extremely short half life of Po-212, athe Po-212 atoms would almost undergo an instant decay into Pb after just decaying from Bi. So most of that 4.0g would have also decayed into Pb-208.

It should be B, as the time period for the transfomation of Po to Pb can be neglected, thus the amount of final Pb we have is going to be relatively dependent on the rate of Bi-212 decay.

[sheepgomoo]

okay!

thank you both for clearing this up for me