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A 40.0 g sample of phosphorus-32 decays until 2.5 g remains. How much time has passed?

A) 4.55 days.
B) 10.91 days.
C) 12.0 days.
D) 24.0 days.

User Olf
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1 Answer

3 votes

Final answer:

Using the half-life of phosphorus-32 which is 14.3 days, it takes 4 half-lives to decay from 40.0 g to 2.5 g, which equates to 57.2 days. None of the answer choices provided matches this calculation.

Step-by-step explanation:

To determine the amount of time that has passed after a given amount of a radioactive isotope has decayed, you use its half-life, which is the time required for half of the isotope to decay. Phosphorus-32 has a half-life of 14.3 days. Starting with a 40.0 g sample, after one half-life (14.3 days), you would have 20.0 g remaining. After another half-life, you would be left with 10.0 g. A third half-life brings you to 5.0 g, and finally, after a fourth half-life, you are left with 2.5 g.

If you calculate the time elapsed, it takes 4 half-lives to get from 40.0 g down to 2.5 g. Thus, the time passed is:
14.3 days/half-life × 4 half-lives = 57.2 days

This value is not listed among the options, suggesting there might be a mistake in the given options or the assumptions made in this calculation.

User Phagun Baya
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