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?

Answer 1

a) We can apply the kinetic energy and work theorem.

k=Coulomb's constant

e=proton charge

r=distance

b) Applying energy conservation:

is slower than light

c=speed of light = 3x10⁸ m/s