Question

A sample taken from a layer of mica in a canyon has 2.10 grams of potassium-40. A test reveals it to be 2.6 billion years old. How much potassium-40 was in the sample originally if the half-life of potassium-40 is 1.3 billion years?

Answer 1

`\boxed{ \text{8.40 g}}`

Step-by-step explanation:

The half-life of K-40 (1.3 billion years) is the time it takes for half of it to decay.

After one half-life, half (50 %) of the original amount will remain.

After a second half-life, half of that amount (25 %) will remain, and so on.

We can construct a table as follows:

No. of Fraction

half-lives t/yr Remaining

0 0 1

1 1.3 billion ½

2 2.6 ¼

3 3.9 ⅛

We see that after 2 half-lives, ¼ of the original mass remains.

Conversely, if two half-lives have passed, the original mass must have been four times the mass we have now.

Original mass = 4 × 2.10 g =
`\boxed{ \text{8.40 g}}`