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41 votes
I need help please ;)

5. The half-life of 1-131 is 8.07 days. If 25 g are left after 40.35 days, how many grams
were in the original sample?

I need help please ;) 5. The half-life of 1-131 is 8.07 days. If 25 g are left after-example-1
User Tung Nguyen
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2 Answers

15 votes
15 votes

Notice that 40.35 is 5 times the half-life of 8.07 days. So in this time, the starting amount x of the sample was halved 5 times until 25 g of it were left, meaning

x/2⁵ = 25 g

Solve for x :

x = 2⁵ • (25 g) = 800 g

User Alex Deckmyn
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2.8k points
14 votes
14 votes

The original mass of the radioactive sample is determined as 800 g.

How to calculate the original mass of the sample?

The original mass of the radioactive sample is calculated by applying the following formula as shown below;

The remaining mass after the decaying period = 25 g

The time of the decay = 40.35 days

The half life of the substance = 8.07 days

The original mass of the radioactive sample is calculated as;

N₀/2ˣ = N

The value of x is calculated as

x = 40.35 days / 8.07 days

x = 5

The original mass of the radioactive sample is calculated as

N₀/2⁵ = 25

N₀ = 32 x 25

N₀ = 800 g

User Cquadrini
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3.3k points