Do Protons and Neutrons Repel Each Other?

The atomic nucleus, the dense core of every atom, is composed of two types of particles: protons and neutrons, collectively known as nucleons. Protons carry a positive electrical charge, while neutrons are electrically neutral. The question of whether these particles repel each other is a logical inquiry based on the principles of electricity. The challenge for nuclear science is explaining how this tiny, crowded core remains bound together despite the intense forces at play. This delicate balance dictates the stability of all matter.

The Paradox of the Nucleus: Electromagnetic Repulsion

In the subatomic world, particles with the same electrical charge exert a powerful repulsive force on one another. Since protons are all positively charged, they naturally push each other away with a force known as electromagnetic repulsion. This force is incredibly strong, especially considering the minuscule distances between protons inside the nucleus, which can be less than one femtometer (\(10^{-15}\) meters). Without an opposing force, the nucleus of any element heavier than hydrogen would instantly fly apart.

The strength of this repulsion is cumulative, meaning that every proton repels every other proton. As the number of protons, or the atomic number, increases, the total disruptive force grows rapidly. This creates a significant paradox: if the nucleus contains multiple positively charged particles, how can any element heavier than hydrogen exist?

This specific type of repulsion only occurs between charged particles. Because neutrons carry no electrical charge, they do not participate in this electromagnetic struggle. A proton and a neutron, or two neutrons, do not experience the electromagnetic force of repulsion.

The Overpowering Glue: The Strong Nuclear Force

The force that holds the atomic nucleus together, overcoming the tremendous electromagnetic repulsion, is the Strong Nuclear Force (SNF). This force is the most powerful of the four fundamental forces in nature, acting as a potent, short-range glue. It is responsible for binding the protons and neutrons into a cohesive unit.

The SNF is approximately 100 times stronger than the electromagnetic force at the extremely short distances found within the nucleus. However, this immense strength comes with a severe limitation: its range is incredibly short. The force effectively drops to zero at distances greater than about \(2.5 \times 10^{-15}\) meters. For comparison, the electromagnetic force has an infinite range.

Crucially, the Strong Nuclear Force is attractive between all nucleons, regardless of their charge. This means it creates an attractive force between a proton and another proton, a proton and a neutron, and a neutron and another neutron. Therefore, the direct answer to whether protons and neutrons repel is no; when they are close enough, they attract each other via the powerful SNF.

The existence of a stable nucleus depends entirely on the SNF being strong enough to overwhelm the electromagnetic repulsion between protons. This attraction ensures that the positive protons and neutral neutrons are all tightly bound together. The force itself is a residual effect of the fundamental strong force that binds quarks together to form the individual protons and neutrons.

How Neutrons Stabilize the Atom

Neutrons play a sophisticated role in maintaining nuclear stability, especially in larger atoms. They contribute to the total attractive force within the nucleus without adding to the repulsive one. Since the SNF acts equally between all nucleons, adding a neutron increases the “glue” without increasing the “push.”

As an atom’s nucleus grows larger, the cumulative electromagnetic repulsion between its many protons increases rapidly. The short-range attractive Strong Nuclear Force must work against this long-range, ever-present repulsion. For lighter elements, like those with fewer than 20 protons, the number of neutrons is roughly equal to the number of protons, maintaining a stable balance.

For heavier elements, more neutrons are required to create the necessary additional attractive force to counteract the rapidly growing proton-proton repulsion. This is why the neutron-to-proton ratio (N/P ratio) increases for stable nuclei as the atomic number climbs. For example, a heavy, stable element like lead-208 has 82 protons but requires 126 neutrons, resulting in an N/P ratio of about 1.5.

This imbalance demonstrates how stability is achieved through a structural compromise. Neutrons are the mechanism the nucleus uses to increase the short-range strong attraction, effectively diluting the effect of the long-range electromagnetic repulsion and holding the entire structure together. When this delicate balance is lost, the nucleus becomes unstable and undergoes radioactive decay.