What Is the Minimum Kinetic Energy Needed for Fusion in Stars?

[fball558]

Homework Statement

Fusion (or "thermonuclear") reactions take place inside a star such as our Sun. One fusion reaction results from a collision between a proton (1H) and a deuteron (2H, the nucleus of "heavy" hydrogen, consisting of a proton and a neutron). When these two nuclei touch, they undergo a nuclear reaction, forming a helium-3 (3He) nucleus (containing two protons and one neutron) and a high energy photon, called a gamma ray.

1H + 2H 3He +

One "unified atomic mass unit", denoted by the symbol "u", is equal to 1.66e-27 kg. The rest mass of the proton is 1.0073 u, the rest mass of the deuteron is 2.0136 u, the rest mass of the helium-3 nucleus is 3.0155 u, and the gamma ray is massless.

If the distance between the centers of the proton and the deuterium nucleus when they are in contact with each other is 2e-15 m, what is the electric potential energy in this state?
(answer is 1.152e-13 J and i know that is right)

now What is the minimum total kinetic energy the particles must have in order that they get close enough to touch each other?
(this is where I am stuck)

The Attempt at a Solution

im stuck really have not tried anything. was thinking conservation of energy, but don't know if that would give me the answer. also not sure what inital velocitys would be so can't use formula.

any ideas??

 

[Imperitor]

Would the answer not be the same as the answer for the first question? (1.152e-13 J)

 

[fball558]

oh... yeah i guess so.
is that because of conservation of energy?
initaly there is no potential and all kenetic and
final state no kenetic and all potential?

 

[Imperitor]

Yes. You nailed it.

 

[fball558]

thanks a lot
Imperitor!