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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 barely touch each other, the distance between the center of the protons = 2*r

where r = radius of protons = 0.878*!0^-15 m

By conserbing energy,

Initial Kinetic energy = Final potential energy

So, (0.5*mv^2)*2 = k*q^2/(2r) <-------- 2r = distance between the protons

So, mv^2 = k*q^2/2r

So, 1.67*10^-27*v^2 = 9*10^9*(1.6*10^-19)^2/(2*(0.878*10^-15))

So, v = 8.86*10^6 m/s <---------answer

b)

Now, total Potential energy = 2*kq^2/r + kq^2/(sqrt(2)*r)

So, mv^2 = 2*kq^2/r + kq^2/(sqrt(2)*r)

So, 1.67*10^-27*v^2 = 2*9*10^9*(1.6*10^-19)^2/(0.878*10^-15) + 9*10^9*(1.6*10^-19)^2/(sqrt(2)*(0.878*10^-15))

So, v = 2.06*10^7 m/s <--------answer

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