An atom is made of positively charged protons and neutral neutrons concentrated

Question

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 10^15 m. How much energy does it take to bring this second proton from very far away to 10^15 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
E= K*q1*q2/r
=(9*10^9)*(1.6*10^-19)*(1.6*10^-19)/(10^-15)
=2.304*10^-13 J

(b)

from the conservation of energy

KE = PE

0.5*m*v^2 = 2.304*10^-13 J
2.304*10^-13 = 0.5*(1.673*10^-27)*v^2
v=1.66*10^7 m/s

(c)

Theproton sped is slower than the speed of light

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