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The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.

What was the initial mass (in mg) of the sample? --------------


What is the mass 7 weeks after the start?-------------

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The half-life of Palladium-100 is 4 days, which means that every 4 days, the amount of Palladium-100 in the sample is reduced by half.

Let's start by finding how many half-lives have passed after 16 days.

16 days / 4 days per half-life = 4 half-lives

This means that the initial mass of the sample was doubled 4 times, since each half-life cuts the mass in half.

So, if the current mass is 2 mg, the initial mass would be:

Initial mass = 2 mg * 2^4 = 32 mg

Therefore, the initial mass of the sample was 32 mg.

To find the mass 7 weeks after the start, we need to find how many half-lives have passed in 7 weeks.

7 weeks = 7 * 7 days per week = 49 days

49 days / 4 days per half-life = 12.25 half-lives

This means that the amount of Palladium-100 in the sample would be reduced to:

Final mass = Initial mass * (1/2)^(12.25)

Final mass = 32 mg * 0.0566

Final mass ≈ 1.8112 mg

Therefore, the mass 7 weeks after the start would be approximately 1.8112 mg.
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