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creekrat48 Group Title

A sample of phosphorus-32 has a half-life of 14.28 days. If 55 g of this radioisotope remain unchanged after approximately 57 days, what was the mass of the original sample?

  • 2 years ago
  • 2 years ago

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  1. Kainui Group Title
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    A half-life is the amount of time it takes for half of the total isotope to decay. So if you know that 55g are left after 57 days and it decreases the total amount by half every 14.28 days, can you set up an equation that describes this?

    • 2 years ago
  2. creekrat48 Group Title
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    thank you

    • 2 years ago
  3. Kainui Group Title
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    You're welcome, if you need more help just ask =D

    • 2 years ago
  4. creekrat48 Group Title
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    wait is it 13.75 g

    • 2 years ago
  5. Kainui Group Title
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    Nope, it can't be simply because you ended up with 55 g of the sample in the end. How could you have 13.75 g decaying away to become more than what you started with?

    • 2 years ago
  6. creekrat48 Group Title
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    ok so i didnt understand how to work this out sorry

    • 2 years ago
  7. creekrat48 Group Title
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    3.99g

    • 2 years ago
  8. Kainui Group Title
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    You're on the right track, but not quite there. 3.99 is not the mass in grams, it is the number of half-lives that the sample has gone through! So now that you know how many times it has split in half, maybe that will help you out more?

    • 2 years ago
  9. creekrat48 Group Title
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    I am not sure where to go from here is it mass to mole

    • 2 years ago
  10. Kainui Group Title
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    Nope, no moles are involved in this problem. I'll type out a better explanation, give me a sec haha.

    • 2 years ago
  11. creekrat48 Group Title
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    OK PLEASE, I HAVE STRUGGLED WITH THIS FOR 2 DAYS AND HAVE SO MUCH MORE TO DO.

    • 2 years ago
  12. Kainui Group Title
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    So you know that the sample has been around for 57 days and the half life is 14.28 days. That must mean that 57/14.28 days. That gave you your 3.99 number of half-lives (not moles) So you have 1/2 to the 3.99 power because you have 1/2 times itself as many times as you have gone through a half-life. 55g = X.5^(57/14.28) Divide 55 by 1/2 to the 57/14.28 power and you should get something like 880g

    • 2 years ago
  13. Kainui Group Title
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    I rounded 3.99 to 4 when I did my calculation, so your answer will be 873.92g if you use 3.99 instead. Hope that helps.

    • 2 years ago
  14. creekrat48 Group Title
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    thank you your the best!!!!

    • 2 years ago
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