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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 3 mg.


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


What is the mass 8 weeks after the start?

Verified Answer :

syed514

16/4 = 4
3 2^4 = 3 16 = 48mg --
initial mass

8 weeks after the start = 87 = 56
56/4 = 14
48(0.5)^14 ~ 0,002929688

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: \(A=a\cdot(\frac{1}{2})^{\frac{t}{h}}\), where,

A = Final amount,

a = Initial amount,

t = Time,

h = Half-life.

Substitute the given values:

\(3=a\cdot(\frac{1}{2})^{\frac{16}{4}}\)

\(3=a\cdot(0.5)^{4}\)

\(3=a\cdot0.0625\)

\(\frac{3}{0.0625}=\frac{3a\cdot0.0625}{0.0625}\)

\(48=a\)

Therefore, the initial mass of the sample was 48 mg.

To find the mass of sample after 8 weeks, we will substitute \(t=8\) in half life formula.

\(A=48\cdot(\frac{1}{2})^{\frac{8}{4}}\)

\(A=48\cdot(0.5)^{2}\)

\(A=48\cdot 0.25\)

\(A=12\)

Therefore, the mass of sample after 8 weeks would be 12 mg.

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