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: Alpha decay vs 12C emission

  1. Sep 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Radium 226 usually decays via three consecutive alpha decays into Pb 214. Show that energetically possibly for radium 226 to decay into 214|86 Pb and 12|6 C but tell why it is highly unlikely.
    Calculate the lifetime of the direct transition as a function of the possibility [itex]\omega[/itex] for the 12C to be assembled in the nuclear parent.
    Hint: lifetime universe : 1.4 10^10 a
    2. Relevant equations
    gamow factor - alpha decay
    fermis golden rule - decay width
    we calculated the one particle into two decay which is
    [itex]\Gamma=\frac{\vec{p_2}}{32 \pi^2 m_a^2} \int{|M^2| d\Omega}[/itex]
    but I have absolutely no idea how to get the M
    3. The attempt at a solution
    I have no idea how to approach this. I can show via the Weizsäcker mass formula that the reaction is energetically possible (funny fact: the alpha decay isn't because the formula calculates the mass for the alpha particle too heavy 4.0071 u instead of 4.0026; 12C is also 12.0026 instead of just 12 - so while its pretty good formula it is actually not good enough) but from then on I am clueless.

    The gamov factor is usually derived for the alpha decay. Can I just take the same [itex]G=\int_R^{r_E}dr\frac{\sqrt{2m_{\alpha}(E-V(r))}d}{\hbar}[/itex] for 12C and then compare the values because they are proportionally to squareroot E ?
    That would be 15 MeV for 12C vs 4 MeV and the formula is [itex]\lambda \propto e^{-2G}[/itex]
    Problem is that the radii for the alpha particle and C are different and therefore the potentials V too. Is the problem really that complicated or am I missing something?
    Anyway, I really would appreciate the help
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted