Question

5. For nuclear fusion to occur, two protons must get closeenough
that, in the terms of quantum mechanics, their wave functionsoverlap
substantially. In quantum mechanics, the radius of a particle hasno
well-defined meaning, but there are quantitites which are analagousto
the radius of a particle, and for a proton, this value is10^-15
meters. The proton's charge is 1.6*10^-19 Coulombs, and thepotential
energy due to the electric repulsive force is expressed as:
E = k q1 q2 / r, where k is the electrostatic constant, 9*10^9Jm/C^2,
q1 and q2 are the charges of the two objects, and r is theseparation
between them.
a) Find the potential energy barrier one needs to overcome tocause
fusion to occur, in this simplified approach
b) At what temperatre will typical atoms have this energy? Hint:you
may find useful the relation <E> =k_B T, which relations themean
energy <E> to the temperature, T, through the Boltzmann'sconstant,
k_B. k_B = 1.38 *10^-23 J/K
c) Compare this temperature with the temperature in the center ofthe
Sun, and make a qualitative statement about how likely anyparticular
atom is
to undergo a fusion in a single near passage to another atom.