Question

krypton-91 is a radioactive substance that decays very quickly remaining after t second, and the decay constant, k, is approximately 0.07 How long will it take a quantity of krypton-91 to decay to 10% of its original amount?

Answer 1

For one thing, "k" should be -.07

You will definitely need the formula in the attached graphic:
time = [natural log (Ending Amount / Beginning Amount)] / k
We'll call beginning amount 100 (for 100 per cent) and ending amount as 10.

time = [natural log (10 / 100)] / -.07
time = [natural log (.1) / -.07
time = -2.302585093 / -.07

time = 32.8940727571 seconds (though we are NOT given any units)

From the attached formula, we can find the half-life from the "k" value and it is:
natural log (.5) / k =
-.69314718056 / -.07 =
9.9 second half - life

To check this answer, we know after 1 half-life the remaining amount is
50%
2 half-lives = 25%
3 half-lives = 12.5%
So, after 3 half-lives (9.9 * 3 = 29.7 seconds), we would have 12.5% of the original Krypton 91

From our calculations, we found that after 32.894 seconds we should have 10% remaining so the calculations seem correct.
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Note Wikipedia says the half-life of Krypton 91 is 8.57 seconds. I'd post a link but my answer would probably get deleted.