1. Not finding help here? Sign up for a free 30min 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!

Nuclear Physics - Uranium decay chain and Bateman equation

  1. Feb 1, 2015 #1
    1. The problem statement, all variables and given/known data

    Calculate the activity of ##^{222}Rn## in an ore sample containing 5g of natural uranium.

    2. Relevant equations

    ##^{238}U## decay chain (to Radon): ##^{238}U\rightarrow^{234}Th\rightarrow^{234}Pa\rightarrow^{234}U\rightarrow^{230}Th\rightarrow^{226}Ra\rightarrow^{222}Ra##

    Bateman equation (for activity of a daughter isotope after a series of decays):

    ##A_n = N_o\sum\limits_{i=1}^{n} c_ie^{-\lambda_it}## where ##c_i=\frac{\lambda_1\lambda_2 ... \lambda_n}{(\lambda_1 - \lambda_i)(\lambda_2 - \lambda_i) ... (\lambda_n - \lambda_i)} \qquad \left(i \neq n\right)##

    3. The attempt at a solution

    Well, I used the known decay constants for each isotope in the decay chain and plugged them into the Bateman equation. Unfortunately, ##c_i## turns out to be negative, giving me a negative number of atoms, which is obviously incorrect. The portion where I simply convert 5g of uranium into total number of atoms is fine. Anyone know where I'm going wrong? I'm assuming ##t=0## since time is seemingly irrelevant to the problem as stated.

    EDIT: I guess I should add that I am getting my decay constants from Wolfram Alpha, but I don't see why it would be giving me anything but the correct values, as they match with other available literature.
     
    Last edited: Feb 1, 2015
  2. jcsd
  3. Feb 2, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    If you start with pure uranium at t=0 then your Radon decays at t=0 will be zero.
    U-238 should be by far the most long-living isotope in your sample. If the sample is old enough (no time is given, so I guess you have to assume that), all other isotopes should be very close to their equilibrium concentrations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Nuclear Physics - Uranium decay chain and Bateman equation
  1. Nuclear Physics decay (Replies: 0)

Loading...