1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Half-life Stuff

  1. Feb 22, 2006 #1
    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
    Am i doing something wrong?
  2. jcsd
  3. Feb 22, 2006 #2
    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?
  4. Feb 23, 2006 #3
    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:

    Now the Co's cancel and you're left with :
    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.
    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)
  5. Feb 23, 2006 #4


    User Avatar
    Science Advisor

    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
  6. Feb 23, 2006 #5
    Thank you HallsOfIvy for being specific for me:)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook