Half Life Questions

[Queen Beach]

Hi Sdn,

I want to start out by saying that I appreciate all the science help and you guys are the best!

Ok, so here are my questions....

Chromium-48 has a short half-life of 21.6h. How long will it take 360 g of chromium-48 to decay into 11.25?
I get how they got the answer, but according to the explanation "1/32 of the original quantity has remained..." How do you get 1/32?

the other question:
Iodine-131 has a half life of 8 days. What fraction of the original sample would remain at the end of 32 days?
I have no clue how they got 4 half-lives because I get 3?

Edit: so for the 2nd ? Do you just go 32/8 then that's how you get 4?
I was doing it like it
32
16
8 that's why I thought 3 half-lives?

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[tyjacobs]

Half life = time it takes for the 50% of the mass of the isotope to decay.

Time it takes to decay = half life * number of half lives the isotope went through

started with 325g of cr-48. Decayed into 11.25g.

1) How many half lives did cr-48 go through?
first, do final mass/original mass to find the fraction of mass remaining
11.25/325 ~ 1/32 (remember, in GC you have no calculator so round!)

second, figure out how many half lives would be needed to get to 1/32 of the original mass.
1/ (2^x) = fraction of mass remaining, where x = # of half lives
1/ (2^x) = 1/32, x = 5

5 half lives * 21.6h (half life) = your answer


second problem:
half life = 8 days (meaning, every 8 days, the mass will decrease by 50%)
32 days has passed
32/8 = 4 half lives have passed (day 8, day 16, day 24, day 32)

1/2^4 = 1/16th the original mass should remain

 

[Queen Beach]

Awesome and thank you! Now I wish I would have watched that last chem video by Mike.