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Chem practice Set 1 Question 11- half life working backwards
Emily_6689
#1 Posted : Sunday, June 13, 2021 10:07:23 AM
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Hi, can someone please explain to me how this works? I cannot figure out how they got the 'half half life would have an activity of 2 + approx 1.4" .... How do they reason the 1.4?

The question:

Half life was 8 days, activity was 1kBq 14 days after treatment, what was activity after one day.


Prep101's explanation: 13 days prior to the measurement, which is roughly 1.5 half lives. Working backward, one half life would have activity of 2kBq [I get that], an additional half life would have activity 2 + approx. 1.4 = 3.4 kBq. [ where they lose me]


Thanks in advance!
INSTR_Katrina_128
#2 Posted : Monday, June 14, 2021 2:38:58 PM
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Agreed... a pretty tricky explanation. I'll give it a shot. 😀

We are told in the passage that the half-life of iodine-131 is 8 days. Currently, the activity is 1 kBq. Now, we want to know what the activity was two weeks IN THE PAST (which is 14 days ago).

The half-life tells us that the activity will DECAY by 50% in 8 days, so if the activity is 1 kBq NOW, then it will be 0.5 kBq in 8 days.

But, we can look at this a little differently ... half-life ALSO tells us how long it takes for the activity to DOUBLE if we go BACKWARDS in time (which we often do in the movies!).

The activity will DOUBLE if we go back 8 days in the past. If the activity is 1 kBq NOW, then it will be 2 kBq 8 days in the PAST.

That means the activity will be doubled AGAIN if we go another 8 days in the past, or 4 kBq.

Wait a minute... that's a total of 16 days in the past, which is pretty stinkin' close to our desired time period of 14 days!

The closest answer is 3.4 kBq, or "a bit less than 4 kBq", which is the correct answer.

Let me know if that helps. 😄

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