if 40 mg of a radioactive substance decays to 5 mg in 12 minutes, what is the half life of the subst.,in min?

Answer 1

Ask yourself...how many times do I have to cut 40 mg in half until I get to 5? Let's see...40 (haven't cut in half yet), 20 (cut once) 10 (cut twice) and then 5 (cut three times!) So, that's thre half-lives that have gone by in 12 minutes. So, since each half-life is the same amount of time, take the time elapsed (12 minutes) and divide it by the number of half-lives (3), and you get 4 minutes per half-life!

You can use this technique to solve problems involving Geiger counters and counts per minute. If the problem has said "A Geiger counter goes from 40 counts per second to 5 counts per second in 12 minutes", you would use the same technique. A half-life is how long a sample of radioactive isotope takes for half of it's atoms to undergo nuclear decay. In one half-life period, each nucleus has a 50% chance of undergoing decay.

Also...when a nucleus decays, it does not disappear, it simply turns into a nucleus of a different element, usually a more stable one. Carbon-14 undergoes beta decay to form nitrogen-14. So, if you started with 40 grams of one type of nucleus (isotope), and end up with 5 grams of that type of nucleus after 3 half-lives, then the missing 35 grams are actually not missing...they have turned into the decay products!

Hope this helps!

Answer 2

Copying Chris F's answer

"40mg -> 20mg = half life = 20mg -> 10mg = 10mg -> 5mg

so it has decyed its half life 3 times in 12 secs, so its half life is 4 seconds"

I think that should be 4 minutes

Answer 3

4 minutes

Answer 4

40 ------> 20 (one half life)
20 -------> 10 (a second half life)
10 --------> 5 (third half life)

If three half lives is 12 minutes then each is 4 minutes

Answer 5

40mg -> 20mg = half life = 20mg -> 10mg = 10mg -> 5mg

so it has decyed its half life 3 times in 12 secs, so its half life is 4 seconds