Question

How much of a 500 g sample of potassium-42 is left after 62 hours? The half time of K-42 is 12.4 hours. Please help.

Answer 1

A "half-life" is an amount of time. It is the amount it takes for total amount of a substance to reduce by half.

So if you have 1 gram of something with a half-live of 2 hours,

after 2 hours (1 half-life), you have \(\dfrac{1~g}{2}=0.5~g\)

after 4 hours (2 half-lives), you have \(\dfrac{0.5~g}{2}=0.25~g\)

We return to your question. how many half-lives have passed?

\(\#~of ~half-lives=\dfrac{time~passed}{half-life}=\dfrac{62~h}{12.4~h}=5~half-lives~have~passed\)

using the logic proposed in the example above, how much of the 500g sample is left?