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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