The radioactive element iodine-131 is commonly used in treating medical problems. It has a half-life of 8.1 days. How long does it take for 99% of a sample of iodine-131 to decay? Give both an exact answer and an approximation correct to three decimal places.
2007-09-04 14:42:01 · 2 answers · asked by Ask or Answer 2 in Science & Mathematics ➔ Chemistry
It's a bit silly to ask for an "exact" answer and one to 3 d.p. when the half-life is only given to two significant figures!
Be that as it may, assuming the half-life to be exactly 8.1 days we have
A(t) = A(0) (1/2)^(t/8.1)
So for 99% to have gone, we need A(t) / A(0) = 1/100, i.e.
(1/2)^(t/8.1) = 1/100
or 2^(t/8.1) = 100
so t = 8.1 log 100 / log 2
= 16.2 / log 2 (logs to base 10, log 100 = 2)
= 53.815 days to 3 d.p.
Note that we are giving an answer to 5 significant figures based on information with 2 significant figures; in reality we can't be more precise than 54 days.
2007-09-04 14:49:41 · answer #1 · answered by Scarlet Manuka 7 · 2⤊ 0⤋
very confusing stuff. try searching using yahoo and bing. that could actually help!
2014-11-05 03:22:57 · answer #2 · answered by ? 3 · 0⤊ 0⤋