Question

a radioactive isotope has a half-life of 2 weeks. if the original of the radiation is 1000 counts per second, how many weeks must elapse until the strength ot the radiation is less than 1 count per second

Answer 1

The period that is the Half Life is the time required for the material to loose half its radioactivity.

Hence for an isotope with a half life of 2 weeks, after 2 weeks there will be half the radioactive decay and hence 1/2 of 1000 counts per second; i.e., 500 counts/second.

Figure out how many periods of 2 weeks you need to wait in order for there to be less than 1 count/second.

If you really can't figure out a formula, do it "by hand", as follows:

1 half-life = 2 weeks = 1000/2 = 500 counts/sec
2 half-lives = 4 weeks = 1000/4 = 250 counts/sec
etc.

Answer 2

Just be careful with the way half-lives add up. To rewrite 2 half-lives,
2 half-lives = 2+2 weeks = (1/2)(1/2)1000 = 250 counts/sec

Answer 3

this application integral...