It's kind of baffling me when I'm encountering this question in this subchapter. 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
argon40, how much potassium40 (t_{1/2} = 1.3 × 10^{9} 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 potassium40 (t_{1/2} = 1.3 × 109 yr) and 2.45 ×
10^{6} mol of argon40. 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.
