Find typical energy of nuclei in solar core

[ck99]

Homework Statement

Calculate the typical energy of nuclei in solar core. Calculate thermal energy required for a proton to overcome the Coulomb barrier and get within range of strong nuclear force (10^-15m)

Homework Equations

None given

The Attempt at a Solution

I have the core temp as 1.5 x 10^6 K. I know that typical nuclei will have mass m_p which is 1.67 x 10^-27kg.

I am sure there must be a simple equation to work this out, but I've never come across it before! I know that the point of the question is to illustrate that fusion reactions would not occur at this temp without quantum tunneling. (Eg typical thermal energy is NOT enough to overcome Coulomb barrier.)

 

[ck99]

A cup of tea and a browse of wikipedia has led me to the following attempt:

Typical energy = 3/2 k_bT = 3.1 x 10^-17J

Coulomb repulsion barrier energy = ke²/r = 2.3 x 10^-13J

Rearrange the first formula to find that the temperature required to break the Couloumb barrier is approx 10^10K.

Is that the correct approach? (Feel embarrassed about posting this now, I knew it would be simple!)