## [SOLVED] Half Life Help

1. The problem statement, all variables and given/known data
The activity of a radioisotope is 3000 counts per minute at one time and 2736 counts per minute 48 hours later. What is the half-life of th radioisotope?

This is where I'm completely lost.
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 Recognitions: Gold Member Homework Help See here for some information: http://hyperphysics.phy-astr.gsu.edu...alfli2.html#c3 http://hyperphysics.phy-astr.gsu.edu...alfli2.html#c2 You first need to figure out the decay constant (represented by $$\lambda$$), which you can do by using the decay equation. Once you have that, you can find the half-life*. The equations you need are in the link. Give it a try and see what you come up with. *Or you could just substitute the expression for lambda (which relates to the half-life) into the decay equation and solve for the half-life all in one go. Same thing.
 $$\ln{\frac {[A]_{0}}{[A]_{t}}} = kt$$ $$t_{\frac {1}{2}} = \frac {\ln{2}}{k}$$ Take 3000 counts as $$A_{0}$$ and 2736 counts as $$A_{t}$$ Also, do you know how the half-life equation is derived? And what connects these 2 equations? *don't forget to convert your units.

## [SOLVED] Half Life Help

ok so $$\ln{\frac {[A]_{0}}{[A]_{t}}} = kt$$ is what I'm going to use to calculate k

and then i use $$t_{\frac {1}{2}} = \frac {\ln{2}}{k}$$ to calculate for $$t_{\frac {1}{2}}$$
 yeah I got 21661 mins which then I converted to hours and that is 361 hours.

 Quote by UWMpanther yeah I got 21661 mins which then I converted to hours and that is 361 hours.
Looks good to me.

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