# Math in Science

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A rock containing a newly discovered fossil is found to contain 5 mg of an unstable form of potassium and 5 mg of the stable element formed from its decay. If the half-life of the unstable form of potassium is 1.3 billion years, how old is the rock? What can you infer about the age of the fossil?

• Math in Science -

well now, it's a bit unclear.

If we are to infer that half of the unstable potassium has decayed into the stable form, then that means one half-life has elapsed, and the rock is about 1.3 gigayears old.

However, the stable element ha a lower atomic weight, so 5mg of the stable element represents more than half of the original unstable potassium. Picky, but that's how things are.

On the other hand, we're dealing with such a long time span that the slight variation probably won't affect much.

Naturally, the fossil is going to be older than the surrounding rock, but probably not by a lot, or the bones would have decayed before being fossilized.

• Math in Science -

mmmhh, that's a tough one.

the fossil is 1.3 billion years old

• Math in Science -

I think the decay is either to Ca-40 or Ar-40 and both have atomic masses so close to K it probably isn't worth worrying about in relation to 1.3 billion years.