I have a few problems that I am stuck on:
1.gallium-68 has a half-life of 68.3 minutes. Are you likely to "run into" gallium-68 in nature? Explain.

2. uranium0238 has a half-life of 4,49 x 10 ^9^ years. Are you likely to "run into" uranium-238 in nature? Where would be the most likely place in the united states to find uranium-238? Explain.

3. a 40.5 g sample of throium-234 has a half-life of 25 days. How much will remain after 240 hours? What percentage of the original amount remains?

4. the half-life of polonium-218 is 3.0 minutes. If you start with 20.0 grams,how long will it take for only 1.0 grams to remain?

1. No, because in 68.3 min, approx one hour, half of it is 'gone'. And since nature was 'here' long ago, I don't think that the answer is yes.

2. Yes, contrary to gallium, uranium takes much more time to decompose to half its mass. For the location, I don't know since I'm not from the US, nor reside there.

For the others, I prefer not to reply for I would suggest you to do a graph. I don't really know the calculations for radioactivity. Perhapd others here will help you.

The formula for doing the math is like this:



So for problem 3:



Note that the units of time must be consistent - here I converted 240 hours to 10 days. So you end up with 75.7% of what you started with.

For the last problem you need to solve for t:



It's easiest to do this using logarithms.