How Does Quantum Mechanics Calculate Proton Interactions at High Temperatures?

[876d34f]

Homework Statement

What is the distance of closest approach between two protons if one is at rest
and the other approaches from really far away with an initial kinetic energy equal to the
average kinetic energy of a proton in a 107K gas? (b) What is the de Broglie
wavelength of a proton with the above kinetic energy? The de Broglie wavelength
is h=p where h is Planck's constant and p is the momentum of the particle. How
does the wavelength compare with the distance of closest approach? (c) Repeat the
above calculations for a proton with 10 times the energy.

Homework Equations

The Attempt at a Solution

for a). I assume you must do an energy relationship so

E1 = E2

1/2mv^2 = 3/2kT = K ==> mv^2 = 3kT ===> v = 3kT/Mp

1/2mv^2 = mgh

h = 1/2gv^2 = 1/(2g(3kt/Mp)^2) = some value... is this the correct approach?

b) the second part using 3kt = mv^2 ===> solve for v then mv is the P = momentum

Lambda = h/p = some value is this correct?

c) just compare values

d) same thing with 10 x the kinetic energy I suppose

 

[llello]

So in part a, you seem to have a "g" floating around. It looks like you assumed the final potential energy is gravitational. The final potential energy should be for electric charges, neglect gravity.