A hypothetical radioactive isotope has a half-life of 10,000 years.?

Question

If the ratio of radioactive parent to stable daughter product is 1:3, how old is the rock containing the radioactive material?

Answer 1

You need to use the formula N =  N_0*exp(-lambda*t) ,

where the half-life = 0.693/lambda, N is how much you have left and N_0 is how much you started with. In your case I guess N/N_0 = 1/(3+1) = 1/4 = 0.25

Answer 2

I believe that it's "~333 years old".

I'm rusty with my physics but if a product is more stable than the substance that produced it then it will in theory age much slower than something radioactive or unstable.

Don't quote me please, I'm only sprouting off the top of my head.

Hoped this helps though.

Answer 3

If the ratio is 1:3, that mean that 1 part in 4 is still radioactive.

In 1 half-life, 1/2 of the stuff turns into the daughter product.

In 2 half-lives, 1/4 of the stuff turns into the daughter product.

So 1/2 plus 1/4 is 3/4, that leaves 1/4 still radioactive.

1/4 is the same as 1 part in 4.

I'm sure you can figure it out from there.