Question

After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remains. What is the half-life of the sample?

Answer 1

Answer on Question #48319 - Chemistry – Other

Question

After 24.0 days, 2.00 milligrams of an original 128.0 milligram sample remains. What is the half-life of the sample?

Answer:

Half-life is a time required for one half the atoms of a radioactive nuclide to decay.

Let’s find out the number of half-lives in 24.0 days:

$$128.0 \ (1/2)^n = 2.00$$ $$(1/2)^n = 0.015625$$ $$n \log 0.5 = \log 0.015625$$ $$n = \log 0.5 / \log 0.015625$$ $$n = 6$$

If 24.0 days have 6 half-lives, then the length of the half-life is:

24 days / 6 half-lives = 4.00 days

Answer: 4.00 days

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