Question #e0dc9

1 Answer
SCooke
Sep 11, 2017

The correct answer should be 624 hours (the data really only provides two significant figures).

Explanation:

This is a common nuclear chemistry problem. I’m not sure if it was correctly posted here.
The relationship between concentration and time for a first-order reaction (radioactive decay) is:
#ln(([A]_t)/[A]_0)) = -kt# where [A] is the concentration at time (t) and k is the rate constant.

Half-life is #t_(1/2) = 0.693/k#
A 10% reduction means that #[A]_t/[A]_0 = 0.9#, so #ln(0.9) = -k xx 95#

#-0.1054 = -k xx 95# ; #k = 0.1054/95 = 0.00111#
Half-life is #t_(1/2) = 0.693/0.00111#; #t_(1/2) = 624.3# hours

CHECK:
#ln(([A]_t)/[A]_0)) = -kt# ; #ln(([A]_624.3)/[A]_0)) = -0.00111 xx 624.3#
IF it is the correct half-life, #[A]_624.3)/[A]_0# = 0.5
#ln(0.5) = -0.693# ; #-0.693 = -0.693# CORRECT

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