1. Deuterium is an isotope of Hydrogen whose nucleus consists of a proton and a

Question

1. Deuterium is an isotope of Hydrogen whose nucleus consists of a proton and a neutron. Deuterium is created in the collision of two protons, a process that requires extremely high temperatures and only naturally occurs in the cores of stars.

A. What speed must two protons initially have when they are a very long distance away from each other in order to just barely touch when they collide?

B. Helium is created from the combination of 4 protons. If each of those protons had the same initial velocity, how fast much each proton be going in order to just barely touch when they all four collide?

Explanation / Answer

A.When they touch, the potential energy of each proton(V)

V=e2/4(2r)= 1.15*10-13J ; where r- radius of the proton(10^-15m). e-charge.

Apply conservation of energy for both particles,

2(mv2/2)=2*V

v=1.17*10^7ms^-1

B. Similarly as above solution, conservation of energy for the whole system

6*V=4(mv2/2) ; [since the potential energy of the system is (1+2+3)*V]

v=1.436*10^7ms-1

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