Why is it impossible for the isotope \({ }_{2}^{2}\) He to exist?

Atomic structure is fundamental to understanding the nature of elements and their isotopes. An atom is composed of a nucleus and an outer shell of electrons. The nucleus contains positively charged protons and neutrally charged neutrons, while the electrons are negatively charged and orbit around the nucleus. The number of protons, termed the atomic number, defines the element. For instance, helium has an atomic number of 2, which means any atom with two protons is recognized as helium.

The mass number of an isotope is given by adding the number of protons and neutrons within the nucleus. Helium's mass number in the discussed isotope is two, corresponding to its two protons. However, the absence of neutrons is unusual and deviates from the general structure of stable atomic nuclei, which typically include one or more neutrons.

Neutrons play a pivotal role in the stability of an atom's nucleus. While they do not contribute to the chemical properties of an element, which are determined by electrons, neutrons provide several critical nuclear functions. They increase the mass of an atom without adding to its charge, and significantly, they mitigate the electrostatic repulsion between protons.

In addition to contributing to the overall mass, neutrons facilitate the strong nuclear force, which is the key to holding the nucleus together. Without neutrons, as is the case with the hypothetical isotope \( {}_{2}^{2} \)He, the protons would repel each other, leading to an unstable or non-existent nucleus.

The strong nuclear force is one of the four fundamental forces of nature and is vital for the stability of atomic nuclei. This force acts between the nucleons (protons and neutrons) in the nucleus, providing the necessary glue that counteracts the repulsive electromagnetic force between like-charged protons.

It is the strongest of the four fundamental forces, but it operates over very short ranges, roughly limited to the distances between neighboring nucleons. The strong nuclear force is approximately 100 times stronger than the electromagnetic force, ensuring that nuclei stay intact despite the repulsive forces trying to tear them apart. Neutrons are essential contributors to this force, which helps to explain why an all-proton nucleus, such as \( {}_{2}^{2} \)He, cannot exist.

The proton-to-neutron ratio is an indicator of isotopic stability. For low atomic number elements, stable isotopes will usually have a proton-to-neutron ratio near unity, meaning the number of protons and neutrons are relatively balanced. As elements get heavier, a higher neutron proportion is generally required to maintain a stable nucleus, due to the increasing electrostatic repulsion between the additional protons.

The ratio also affects the nuclear binding energy, which is the energy needed to hold the nucleus together. For example, the non-existence of the isotope \( {}_{2}^{2} \)He indicates a problem with this ratio, as it has two protons and no neutrons, which is insufficient to overcome proton repulsion and maintain stability.