Okay, here's the deal:

I have a substance that reduced in number from 50, to 28, to 17, to 5, and then to 2. In percentages, it went from being 100% present, to 56%, then 34%, 16%, 10%, and finally 4%. What is the half-life? The substance was pieces of candy- I'm supposed to pretend it was a chemical or something going through radioactive decay. The period of time between each loss of candy was 10 seconds consistently.

Could you write out your work, I want to understand how to solve this, not just get an answer. Thanks so much!!

Question

Okay, here's the deal: 

I have a substance that reduced in number from 50, to 28, to 17, to 5, and then to 2. In percentages, it went from being 100% present, to 56%, then 34%, 16%, 10%, and finally 4%. What is the half-life? The substance was pieces of candy- I'm supposed to pretend it was a chemical or something going through radioactive decay. The period of time between each loss of candy was 10 seconds consistently. 

Could you write out your work, I want to understand how to solve this, not just get an answer. Thanks so much!!

aaronq · Answer

use the first-order integrated rate law to find the decay constant:

$\large ln[A]_t=-kt+ln[A]_o$

where $ln[A]_o$ is the initial concentration of the substance
$k$ is the decay constant
$t$ is time
$ln[A]_t$ is the concentration of substance at time $t$

then use: $\large t_{1/2}=\dfrac{ln(2)}{k}$ to find the half-life after you've found $k$.

$t_{1/2}$ is the half-life