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

1 Answer
Tony T.
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 #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
=)

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