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

May 24, 2017

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 $\frac{1}{{2}^{n}}$ 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 ($\frac{1}{2}$ or $\frac{1}{2} ^ 1$)
after 2 half lives, you are left with a quarter of the sample ($\frac{1}{4}$ or $\frac{1}{2} ^ 2$)
after 3 half lives, you are left with an eighth of the sample ($\frac{1}{8}$ or $\frac{1}{2} ^ 3$)
therefore 3 half lives have occured to give $\frac{1}{8}$.
34.5 minutes divided by 3 is 11.5

$\frac{34.5}{3}$ = $11.5$

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