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I am just starting with radioactivity and I came upon this statement:

"Since the nucleus is stable, this means that there is some attractive force at work in the nucleus and that its magnitude exceeds that of the repulsive electrostatic force which binds the protons and neutrons inside the nucleus."

So, it got me curious to think what would happen in the aforementioned case.

P.S. I guess you can understand I'm a beginner, so I would request logical and theoretical explanations rather than mathematical ones.

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    $\begingroup$ Then the nucleus would not be bound - the protons could wander off on their own (slowly, rather than flying apart from the Coulomb force). $\endgroup$ – Jon Custer Feb 11 at 15:29
  • $\begingroup$ @Jon Custer This helped! $\endgroup$ – Paul Feb 11 at 15:51
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Firstly, it is necessary to mention that nuclei are not the only places where the attractive and repulsive forces are in competition. Molecules and solids are other obvious examples: e.g., in a metal the positively charged ions repel each other, just like the negatively charged electrons do. Yet, the system as a whole is stable, due to the attractive forces between these two, and exchange interaction (without exchange the system would be still unstable, as stated by the Earnshaw theorem).

What makes nuclei different is that the attractive forces between nucleons are of different nature than the electrostatic forces, and have different dependence on the distance, roughly modelled by the Yukawa potential. Thus, the attractive forces dominate at very short distances, but quickly decay with distance. Moreover, these forces act not only between positively charged protons, but also between protons and neutrons. In particular, the system of two protons could not be stable, but the system of a proton and a neutron (deuterium), of two neutrons and a proton (tritium) and of two protons and a neutron (Helium-3 nucleus) are all stable (or have very ling lifetime).

To summarize:

  • Nuclear and electrostatic forces have different dependence on a distance, so they couldn't cancel each other completely - only in certain spatial configurations.
  • Nucleon systems where nuclear forces do not dominate (at short distances) are unstable.
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