Question

A paleontologist estimates that when a particular rock formed, it contained 12 mg of the radioactive isotope potassium-40. The rock now contains 3 mg of potassium-40. The half-life of patassium-40 is 1.3 billion years. About how old is the rock?a. 0.4 billion yearsb. 0.3 billion yearsc. 1.3 billion yearsd. 2.6 billion yearse. 5.2 billion years

Answer 1

d. 2.6 billion years.

Step-by-step explanation:

The half-life of a radioactive element it's the time that its mass decreases by half, or, by 0.50. So, if there is 10 mg of A when the mass became 5 mg, it will have past one half-life. The next half-life will decrease by half the actual mass, so it will give 2.5 mg, which is 0.5x0.5 of the initial mass.

So, the number of half-life (n) can be calculated for:

`M =(Mo)/(2^(n) )`

Where M is the residual mass and Mo the inital mass, so:

`2^n = (12)/(3)`

`2^n = 4`

`2^n = 2^2`

n = 2

So, it has passed 2 half-lives. If one half-life is 1.3 billion years, two must be 2.6 billion years, which is the age of the rock.