Written homework, due at start of studio 2a(means week=2, studio=rst) In lecture

Question

Written homework, due at start of studio 2a(means week=2, studio=rst)
In lecture Monday we learned that the voltage at a distance R from a charge
Q is V (R) 9 109Q=R when we call V (1) = 0. We'll use this now to
learn a bit about why the sun shines. (Well, the sun shines because it is a hot
ball of gas, and hot things shine. Why it stays hot is what concerns us in this
problem.) The reason it stays hot is this: protons in the sun can sometimes
get close enough together for a nuclear reaction to occur; that starts a cycle in
which hydrogen is turned into helium; the energy released in the cycle is what
keeps the sun hot. But there is a problem: the reaction can only occur if the
protons get close together, but they are both positively charged, so they repel
each other. This problem asks the question: How close do two protons get, on
the average?"
The center of the sun is mostly hydrogen, but it is so hot (T 107 ?C) that
the hydrogen is all ionized, so we can just think of a gas of hot protons and
electrons. The last week of EP1 we learned that the average kinetic energy of a
particle in a gas is 3kT=2, with k = 1:38 10?23 J/?K. (Does it matter in this
situation whether we use degrees C or degrees K?)
Consider then a head-on collision between two protons moving at the typical
speed at this temperature. How close do they come before the repulsion
makes them stop and turn back? Don't worry about factors of 2 or 4 in your
answer; we are just making a rough estimate.
1

Explanation / Answer

so far apart each proton has 3/2 kT when they get close all that kinetic turns to potential 9E9 q^2/r so 2*(3/2 kT) = 9E9 q^2/r 2*1.5*1.38E-23*(107+273.15)=9E9 (1.6E-19)^2 /r solve for r, r=1.46E-8 m

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