# 32P has a half life of 14.26 days. How many grams remain after 42.78 days?

32P has a half life of 14.26 days. If you initially have 100.0g of 32P how many grams of it remain after 3 half life periods i.e. after 3(14.26) = 42.78 days

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You could use logarithms for related questions like this

Af = Ao(0.5)^(x/t) [Note: you use 0.5 because it's half-life that you're dealing with]

Af= final amount
Ao = initial amount
x = # of periods ( in this case, 3)
t = period of each half life

Af = 100.0(0.5)^(42.78/14.26)

Or simply Af = 100.0(0.5)^3 since you know 3 half life periods have occured.

Af = 12.5g
After the first half-life: 1/2
After the second: 1/2 of 1/2
After the third: 1/2 of 1/2 of 1/2 = 1/8th

I don't know if there will be a change in the overall weight because this is just a decay into another substance so at the end of 3 half-life periods, the total weight may still be 100.0g of something else.

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