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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