6. (20 pts.) An atom is made of positively charged protons and neutral neutrons

Question

6. (20 pts.) An atom is made of positively charged protons and neutral neutrons concentrated in a nucleus, while negatively charged electrons orbit around them. If I want to make a Helium atom out of two Hydrogen atoms, I am going to have to have to get 2 Hydrogen atoms very close together so that they can form a new nucleus. This is a process called nuclear fusion, and it takes a lot of energy.

a) If, in order for this to happen, I have to bring the two protons to within 1015 m. How much energy does it take to bring this second proton from very far away to 1015 m from the first proton?

b) With how much speed would I have to shoot this proton toward the first in order for it to make it?

c) Is that speed faster than or slower than the speed of light?

Explanation / Answer

a)
Energy required = potential energy of system
= K*q1*q2/r^2
=(9*10^9)*(1.6*10^-19)*(1.6*10^-19)/(10^-15)
=2.304*10^-13 J
Answer: 2.304*10^-13 J

b)
This must be the kinetic neergy of proton
KE = 0.5*m*v^2
2.304*10^-13 = 0.5*(1.673*10^-27)*v^2
v=1.66*10^7 m/s
Answer: 1.66*10^7 m/s

c)
This is slower than the speed of light

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