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Help please

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?-------------

User JohnnyFun
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1 Answer

3 votes

Answer:

  • 32 mg
  • 6.57 µg or 0.00657 mg

Explanation:

You want the initial mass, and the mass after 7 weeks, of a sample of Palladium-100 with a half-life of 4 days and a mass of 2 mg after 16 days.

Model

The amount of Palladium-100 remaining after t days can be modeled by ...

a(t) = (initial amount)·(1/2)^(t/(half-life period))

a(t) = a0·(1/2)^(t/4) . . . . . . where t is in days, and a0 is the initial amount

Application

Using this model to find a0, we have ...

a(16) = 2 mg = a0·(1/2)^(16/4) = a0/16

a0 = 32 mg . . . . . . multiply by 16

The initial mass of the sample is 32 mg.

7 weeks

The mass after 7 weeks (49 days) will be ...

a(49) = (32 mg)·(1/2)^(49/4) ≈ 0.0065698 mg

The mass after 7 weeks is about 6.57 µg or 0.00657 mg.

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Help please The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-example-1
User Edthix
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