The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced to a mass of 7 mg. A.) What was the initial mass (in mg) of the sample?

B.) What is the mass (in mg) 4 weeks after the start?

You may enter the exact value or round to 4 decimal places.

9514 1404 393

  A) 448 mg

  B) 3.5 mg

Step-by-step explanation:

24 days is 24/4 = 6 half-lives. That is, the mass of 7 mg is 2^-6 times the initial mass.

A) The initial mass is 2^6×(7 mg) = 448 mg

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B) 4 weeks is 28 days, or 7 half-lives. The remaining mass will be half the amount after 6 half-lives.

  (7 mg)/2 = 3.5 mg . . . . remaining after 4 weeks