- #1
Zain Syed
- 7
- 0
Hey guys, I'm working on a homework problem about nuclear fusion in stars and am..stuck on the first step: calculating the temperature needed for protons to come within 2 fm of one another and overcome Coulomb repulsion.
1. Homework Statement
Given that the protons have an average kinetic energy (3/2)kbT, and in the Boltzmann distribution there will be some protons of 4 times that energy, show that a temperature of about a billion degrees Kelvin is needed in order for the protons to overcome the Coulomb repulsion and approach each other within 2 fm.
avg KE = (3/2)kbT
Coulomb Barrier: U = ke2/r
I calculated U to be 1.4 * 106eV. I then plugged this in as an inequality, where the avg KE > U and solved for T, which I found to be 1.08*1010K.
I'm certain I missed something, or a lot of something, but I don't know what that is. I'm meant to use the finite-structure constant α = 1/137, right?[/B]
1. Homework Statement
Given that the protons have an average kinetic energy (3/2)kbT, and in the Boltzmann distribution there will be some protons of 4 times that energy, show that a temperature of about a billion degrees Kelvin is needed in order for the protons to overcome the Coulomb repulsion and approach each other within 2 fm.
Homework Equations
avg KE = (3/2)kbT
Coulomb Barrier: U = ke2/r
The Attempt at a Solution
I calculated U to be 1.4 * 106eV. I then plugged this in as an inequality, where the avg KE > U and solved for T, which I found to be 1.08*1010K.
I'm certain I missed something, or a lot of something, but I don't know what that is. I'm meant to use the finite-structure constant α = 1/137, right?[/B]