Question

If 1/8 of an original sample of krypton-74 remains unchanged atter 34.5 minutes, what is the half life of krypton-74?

Answer 1

11.5 minutes (11 minutes, 30 seconds)

Explanation:

this is a nice easy half-life calculation as no equation is required.
if you see one over two the power of n `1/(2^n)` then you know it is an exact multiple of half lives.
you start off with 1 multiple of the sample (the entire sample).
after 1 half life, you are left with half of the sample (`1/2` or `1/2^1`)
after 2 half lives, you are left with a quarter of the sample (`1/4` or `1/2^2`)
after 3 half lives, you are left with an eighth of the sample (`1/8` or `1/2^3`)
therefore 3 half lives have occured to give `1/8`.
34.5 minutes divided by 3 is 11.5

`34.5/3` = `11.5`

so the half-life of `""_36^74 Kr` is 11.5 minutes
=)