Half life problem

[tabitha6269]

Hello everyone. I was hoping to get help with a problem I came across regarding half lives. I understand the first two parts of the question, however, am struggling with the third portion.

The half-life of chromium-51 is 28 days. If the sample contained 510 grams, how much chromium would remain after 56 days? How much would remain after 1 year? How much was present 168 days ago?

The answer yields 32000 g, however, I have no idea how they arrived at this answer. Could someone please help! Thanks

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[Ari Rezaei]

The trick is they're asking 168 days ago. This means you have to calculate the original sample and assume the 510 grams is the final mass of the sample.

The formula for half life is (Final amount) = (initial amount) * (1/2)^(time/half life)

Final amount = 510 g
Initial amount = x
time = 168 days
half life = 28 days

510 = x * (1/2)^(168/28)
510 = x * (1/2)^(6)
510 = x * (0.015625)
510/0.015625 = x
32,640 g = x

To check our work, just take 32640, and divide it in half 6 times. You could also use this as a short cut, once you find out they're asking what the mass was 6 half lives ago, you can just multiply your mass by 2 six times to arrive at 32640g.

 

[alexis2010]

There are 2 ways you can do this:
1st: Know the half life formula which is: A=A0(1/2)^(t/half life) where A0 is the original amount
2nd: work backward🙁 If you don't know the half life formula)
168/28 = 6
then multiply by 2 6 times
510*2 = 1020
1020*2=2040
2040*2=4080
4080*2=8160
8160*2=16320
and finally: 16320*2=32640