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Thread: Boltzmann Factor of Proton Proton chain

  1. #1 Boltzmann Factor of Proton Proton chain 
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    Join Date
    Jan 2009
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    Agh! Keep getting ridiculously low boltzmann factors for the proton proton chain. Help me prove that something similar to quantum tunneling occurs in the sun!

    Potential energy you need to put in to make two protons get close enough for fusion
    :


    V = KQq/r
    The charges are the same so we can simplify the two Qs to Q^2.
    Charge on a Proton = 1.6 x 10^-19 C
    Distance at which strong force is dominant = 5 x 10^-15 m (http://nu.phys.laurentian.ca/~fleuro...te/coulomb.png)

    K = Coulombís Constant = 9 x 10^9 Nm^2C^-2
    k = Boltzmannís Constant = 1.38 ◊ 10^-23 m^2 kg s^-2 K^-1

    V = Potential Energy = (9 x 10^9 x (1.6 x 10^-19)^2) / (5 x 10^-15) = 4.61 x 10^-14 J

    4.61 x 10^-14 J = Ĺmv^2 = 3/2 x kT

    4.61 x 10^-14 J /1.5k = T = 2.23 x 10^9 K

    Boltzmann factor = e-ε/kT
    = e^(-4.61 x 10^-14 J / (1.38 x 10^-23 x 2.23 x 10^9))
    = 4.482

    4.482 has to be wrong right?


    I had a simple dream: a dream to kill all humans, and this is how you repay me?
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