phost

It's kind of baffling me when I'm encountering this question in this sub-chapter. It's just unusual. So I really need your help :D

1. The problem statement, all variables and given/known data
If a rock sample was found to contain 1.16 × 10^-7 mol of
argon-40, how much potassium-40 (t_1/2 = 1.3 × 10⁹ yr)
would also have to be present for the rock to be 1.3 × 109
years old? See assumption in Problem 14.84.

And the problem 14.84 question is ...

A 500 mg sample of rock was found to have 2.45 × 10^-6
mol of potassium-40 (t_1/2 = 1.3 × 109 yr) and 2.45 ×
10^-6 mol of argon-40. How old was the rock? (Hint: What
assumption is made about the origin of the argon-
40?)


2. Relevant equations
k = In 2/t_1/2

3. The attempt at a solution
I just find out that the both K and Ar in periodic table have a closely enough molecular mass, which is 40 g/mol (39,1 for K and 39,95 for Ar). But it just weird when the molecular mass is multiplied with each moles of Ar and K to find mass, because it doesn't add up for 500 mg. Also I don't have any idea what does the t_1/2 works for. Of course we could find the rate constant from the equation before for it.