Question

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.

Answer 1

16/4 = 4 3 * 2^4 = 3 * 16 = 48mg --
initial mass 8 weeks after the start = 8*7 = 56 56/4 = 14 48*(0.5)^14 ~ 0,002929688

Answer 2

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.