The half-life of Palladium-100 is 4 days...?

Question

The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 2 mg.

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

What is the mass 4 weeks after the start?

Answer 1

Let

T = 4 days be the half-life,

t be time elapsed, e.g., 12 days or 4 weeks,

m(t) be the mass after time t.

The general formula is

m(t) = m(0)2^-t/T

If you prefer to think in terms of the example,

then 12 days (being 3 times the half-time) caused

3 halving of the initial quantity;

that is, reducing the initial quantity by a factor of 8.

To answer the first problem

2mg = m(0)2^-12/4

m(0) = 2mg x 8 = 16mg

To answer the second question

m(28) = 16mg x 2^-28/4= 16 mg x 2^-7 = 0.125mg