An Electron Can Not Exist Inside The Nucleus

 This is one of the issues which lead to the advancement of quantum mechanics in the 1920's. Great job thinking fundamentally. The short answer is they do, yet quantum mechanics/enchantment prevents them from remaining there. The long answer includes some history and a concise talk of quantum mechanics.

Old style mechanics gives a convenient recipe to figuring the pace of intensity dispersal brought about by a quickening charged item. It is known as the larmor law, and is recorded underneath:

[math]P = {2 \over 3} {q^2 a^2 \over 6 \pi \epsilon_0 c^3}[/math] 

This works astoundingly for such things as electrons quickening in an attractive field; one can, for example, gauge the force yield of a magnetron utilizing this recipe. Nonetheless, it was known around 1920 that the structure of the iota must be that of electrons turning around molecules in particular orbitals: the circle model or "bohr" model of the particle. Some cunning individuals, utilizing what was known at the time, endeavored to discover to what extent those electrons should last. Oh dear, for practically all issue the appropriate response was well under a second!

This situation, I expect, is a lot of like the chain of rationale prompting this inquiry. The answer for the issue was the improvement of quantum mechanics.

Quantum mechanics doesn't loan itself well to analogies, yet I can clarify what it does. Essentially, it speaks to the molecule in a vitality arrangement, and afterward asks what potential states can the electron be in. The outcome is a likelihood, not a way, with the end goal that you can just solicit "What is the likelihood of the electron being here," not "where is the electron." The portrayal for the least complex molecule, the hydrogen iota, is:

[math]-\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial\psi}{\partial r}\right)+\frac{1}{r^2\sin\theta}\frac{\partial}{\partial\theta}\left(\sin\theta\frac{\partial\psi}{\partial\theta}\right)+\frac{1}{r^2\sin^2\theta}\frac{\partial^2\psi}{\partial\phi^2}\right]-\frac{Ze^2}{4\pi\epsilon_0r}\psi=E\psi[/math] 

(You don't need to get this)

Significantly, the yields of this dreadful math are a progression of conditions in space which are autonomous of each other. What's more, in principle, one can speak to ANY electron position or design as a total of these outcomes. For hydrogen, a few of the states are:

The best approach to peruse the outline above is to comprehend the surfaces demonstrate where the likelihood is equivalent of finding the electron, and that the core is at the focal point of the shape. Presently, high n and high l states have the property of regularly having no likelihood at the core: the diagrams "cease to exist" at these areas. For these shapes, it tends to be said the electrons don't stretch out inside.

However,for the l=0 m=0 states specifically there is in actuality likelihood in the core. A particle with an electron in this state will have a nonzero likelihood of the electron being inside the core. It turns out this is significant, and prompts such impacts as the "Hyperfine cooperation."

Presently, coming back to the first inquiry: for what reason don't they all fall in? Essentially, the math disallows it. One can scientifically develop a circumstance wherein all electrons are spoken to at the focal point of the core; in any case, over the long haul the electrons speedily "flee" from the center.