Potassium-40 has a half-life of 1.3 billion years. as the potassium-40 isotope decays, it becomes argon. if a rock was formed with 12 g of potassium-40, approximately how long would it take for 75% of the potassium-40 to be replaced by argon?

2.6 billion years.

Explanation:

The half live is given by:

Ak40 -(Ak40/2^n) ÷ Ak40/2^n = number of atoms of argon.

But there is 12g of argon

Atomic mass of argon/ 12g = number of atoms of argon

36/12 =3 atoms

Ak40 -(Ak40/2^n) ÷ Ak40/2^n= 3 atoms

Dividing by Ak40 gives

2^n-1 ×2^n=3

2^n =3+1

2^n=4

2^n=2^2

n=2

This means that it will take 2 half lives in order for the sample to contain 12g of argon.

2 halflives× 1.3 billion years/1 half life

=2.6 billion years

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