Calculating Half-Life: 50mg to 10mg in 18.4 Days

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Homework Help Overview

The discussion revolves around calculating the time required for a 50 mg sample to decompose to 10 mg, given a half-life of 18.4 days. The subject area includes concepts of half-life and exponential decay in the context of chemistry or physics.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants explore different equations related to half-life and exponential decay. The original poster attempts to manipulate an equation but questions their approach. Others suggest alternative methods and identify potential errors in the original poster's reasoning.

Discussion Status

Participants are actively engaging with the problem, offering guidance and alternative approaches. There is a recognition of errors in the original poster's setup, and some participants provide insights into the correct application of half-life equations.

Contextual Notes

There is an emphasis on understanding the correct formulation of the half-life equation and the implications of the calculations involved. The original poster expresses uncertainty about their method, indicating a need for clarification.

runicle
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Something has a half-life of 18.4 days. How much time will a 50-mg sample take to decompose to 10 mg?
My steps
50(1/2)^n/18.4 = 10(1/2)^n/18.4
25^n/18.4 = 5^n/18.4
(5^2)^n/18.4 = 5^n/18.4
5^2n/18.4 = 5^n/18.4
Exponent view
2n/18.4 = n/18.4
2n-n = 18.4/18.4
n=1
Am i doing something wrong?
 
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half life equation is
[tex]q(t) = q_{0} 2^{-t/\tau}[/tex]
where q(t) is the quantity after time t,
q0 is the initial quantity
tau is the half life

do u see your mistake?
 
Y=CoE^kt
Co = initial amount
Y= what amount is left
K= rate
T= time
First you have to find the rate
Since in 18.4 days you will have 1/2 left you set it up like this:

1/2Co=CoE^kt
Now the Co's cancel and you're left with :
1/2=e^kt
t=18.4
1/2=e^k(18.4)
Take the natural log of both sides now
ln(.5)=lne x 18.4k
-.6931471806 = 1 x 18.4k
divide by 18.4
k = -.0377
Now you must find the time it takes to go from 50 to 10.
10=50e^kt
k we know = -.0377 and we're looking for t

You should be able to figure it out from here.(sorry if my work doesn't look fancy, I'm new to this stuff - I'll pick it up eventually)
 
This: 50(1/2)^n/18.4 = 10(1/2)^n/18.4 is your error.
You want to end with 10 g so you want
50(1/2)^(n/18.4)= 10
 
Thank you HallsOfIvy for being specific for me:)
 

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