Let's say we have a isotope 222Rn that will change, after more than 3 days, into a 218Po because it will release a "small 4He nuclei" at 5 % the speed of light.. I've got 2 questions.
Have a look at this table of isotopes
The half life for 222Rn is 3.8235(3) days. Half life means the time it takes for a given N number of atoms of 222Rn to decay so that only N/2 222Rn are left in the sample and the other N/2 have become 218Po.
First, what is going on in those 3 days, what is happening. Does the nuclei is "unstable", vibrating ?
The sample of Radon is diminishing at the rate given by the life time, random atoms decaying according to the exponential probability curve fixed by the half-life . At a time t, each individual atom will either have decayed or it is still intact as a gas of the sample.
Second, where does the electron go?
Radon is a gas, and the two electrons left orphan around the radon when it decays into polonium will form double negative ionized atoms either on polonium or other not-yet-decayed radon in the gas. There are energy levels available on atoms over the filled with electrons shells. The alpha particle will find little scattering targets in the gas and will leave the sample as radiation doubly positive charged. When it loses energy it will pick up electrons from the air and be a Helium gas. The ionized radon/polonium will transfer the electrons to the gas or the container surrounding it.