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Consider ${\rm He}^{2+}$ as a example. It has 2 protons and 2 neutrons but no electrons. How is that ion can exist as an atom, and how can we account for its stability?

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    $\begingroup$ Why do you believe it wouldn't be stable? Electrons have very little to do with the stability of atoms. $\endgroup$ – Chris Oct 20 '17 at 6:08
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    $\begingroup$ This is also called alpha particle. It is the nucleus of helium. What do you mean by "how is that ion existing as an atom"? The alpha particle is very stable because it has a high binding energy per nucleon. This is due to the strong nuclear force. $\endgroup$ – Andrei Geanta Oct 20 '17 at 6:09
  • $\begingroup$ An atom is electrically neutral, thus the question has a simple NO as an answer. $\endgroup$ – DanielC Dec 11 '17 at 16:38
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Atoms are formed by a nucleolus with Z protons and an equivalent Z number of electrons. The nuclear mass (A) equals the mass of its protons plus the mass of its neutrons minus the mass lost as energy when binding all these protons and neutrons in the atom nucleus. When an atom loses $\rm n$ number of electrons, it becomes an ion with a ${\rm +n}e$ charge or ${\rm -n}e$ charge otherwise, with $e$ being the fundamental charge.

There are two ways protons can be bound close to each other:

The first form is for example the case that happen when a proton with an electron (Hydrogen atom) bounds to an equal partner by way of covalent forces and creates the hydrogen molecule ($\rm H_2$). In this setup, these protons could not be bound together without its electrons since electron sharing is causing the bound. Instead of hydrogen atom this example could be made using two deuterium atoms forming a deuterium molecule with 2 protons, 2 neutrons and 2 electrons.

The second form is that protons could be bound together by means of strong nuclear force. This is one of the four fundamental forces and is of a different nature than the covalent bound used before. Therefore, the two protons of the Helium ($\rm He$) atom are not bound by the same forces as the two protons in the deuterium molecule, even though both structures have 2 protons, 2 neutrons and 2 electrons. This is the reason why they can exist even without electrons in the form of an helium ion ($\rm He^{2+}$).

It’s stability is accounted by the immense energy that is lost when the four nucleons are bound together. Mathematically speaking,

$${\rm ΔE=(2m_p+2m_n-m_{He^{+2}})}c^2$$

Where,

$\rm ΔE$ is the alpha particle’s ($\rm He^{+2}$) binding energy, $\rm m_p$ is the proton mass, $\rm m_n$ is the neutron mass, $\rm m_{He^{+2}}$ is the alpha particle mass and $c$ is the speed of light.

Thus, one needs to supply all that energy back to the $\rm He^{2+}$ nucleus in order to dismantle it.


PS: The particle $\rm He^{2+}$ when emitted by some radioactive materials is known as alpha radiation or alpha particle.

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