It’s similar to forces between neutral atoms where it’s somewhat easier to explain. Imagine you have two atoms (left, right) where each atom has a positive and a negative electric charge in it and some random orientation:
+ + –
–
The positive charges repel each other, the negative charges repel each other, but pairs of positive and negative charges attract each other. That makes them rotate that way:
+ –
– +
Now the attractive pairs have a slightly shorter distance than the repulsive pairs. Shorter distance means stronger force. That makes both atoms attract each other.
For the strong interaction you have something similar. Protons and neutrons are made out of quarks which have a “color charge” and different charges attract each other.
If you have a free proton and a free neutron then they attract each other via this process. They can collide and form deuterium. The energy of the collision is released, in this case as radiation. Most nuclear interactions are more complicated but the general idea is the same. You look at how much everything attracts each other and how much energy the nucleus has overall. In addition to the strong interaction you also need to consider that all the protons repel each other. If the overall energy decreases in a reaction then the difference is set free – as radiation or as fast-moving particles flying away.
For very heavy nuclei you have tons of protons all repelling each other, so splitting the nucleus and letting half the protons fly away from the other half releases energy, a little bit like expanding a spring can accelerate a mass that is being pushed away.
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