A rock sample has 6 billion K-40 atoms (parent isotope), and 6 billion Ar-40 atoms (daughter isotope)...?

Question

 After two half-lives, what is the content of the rock sample?

1) 9 billion K-40 atoms and 3 billion Ar-40 atoms.

2) 1.5 billion K-40 atoms and 10.5 billion Ar-40 atoms.

3) 0 K-40 atoms and 12 billion Ar-40 atoms.

4) 0.75 billion K-40 atoms and 11.25 billion Ar-40 atoms.

5) 3 billion K-40 atoms and 9 billion Ar-40 atoms.

Answer 1

A = A₀ (1/2)^(t/h)

a = (1/2)² = 1/4 amount left

6 billion * 1/4 = 1.5 billion K40

So answer B is the only one possible.

Answer 2

(6 billion atoms K-40) x (1/2)^2 = 1.5 billion atoms K-40 remain

((6 billion atoms initially) - (1.5 billion atoms remain) = 4.5 atoms K-40 decayed

Each atom of K-40 that decays produces one atom of Ar-40, so

(6 billion atoms Ar-40 initially) + (4.5 billion atoms Ar-40 additional) =

10.5 billion atoms Ar-40 at the end of two half-lives of K-40

So answer 2).

Answer 3

2) 1.5 billion K-40 atoms and 10.5 billion Ar-40 atoms.