Answer:
1. 48 mg.
2. 12 mg.
Step-by-step explanation:
We have been given that the half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 3 mg.
Half-life formula:
, where,
A = Final amount,
a = Initial amount,
t = Time,
h = Half-life.
Substitute the given values:
![3=a\cdot(\frac{1}{2})^{\frac{16}{4}}](https://tex.z-dn.net/?f=3%3Da%5Ccdot%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7B16%7D%7B4%7D%7D)
![3=a\cdot(0.5)^{4}](https://tex.z-dn.net/?f=3%3Da%5Ccdot%280.5%29%5E%7B4%7D)
![3=a\cdot0.0625](https://tex.z-dn.net/?f=3%3Da%5Ccdot0.0625)
![\frac{3}{0.0625}=\frac{3a\cdot0.0625}{0.0625}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B0.0625%7D%3D%5Cfrac%7B3a%5Ccdot0.0625%7D%7B0.0625%7D)
![48=a](https://tex.z-dn.net/?f=48%3Da)
Therefore, the initial mass of the sample was 48 mg.
To find the mass of sample after 8 weeks, we will substitute
in half life formula.
![A=48\cdot(\frac{1}{2})^{\frac{8}{4}}](https://tex.z-dn.net/?f=A%3D48%5Ccdot%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B%5Cfrac%7B8%7D%7B4%7D%7D)
![A=48\cdot(0.5)^{2}](https://tex.z-dn.net/?f=A%3D48%5Ccdot%280.5%29%5E%7B2%7D)
![A=48\cdot 0.25](https://tex.z-dn.net/?f=A%3D48%5Ccdot%200.25)
![A=12](https://tex.z-dn.net/?f=A%3D12)
Therefore, the mass of sample after 8 weeks would be 12 mg.