Question

Question #e0dc9

Answer 1

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