Confusion in Positron Decay

Question

As we know, in a positron decay, by the involvement of weak forces, a proton converts into an neutron, emitting a neutrino and a positron, all of this happens inside the nucleus.

1. Why doesn't the emitted positron, while coming out of the nucleus, and passing through the electron cloud annhiliate an electron?

2. Now, the new nucleus has a proton less and a neutron more. Will the atom still remain electrically neutral? If yes, then the total protons must be equal to the electrons, since one proton is reduced in the interaction, one electron also must reduce, where does this electron go?

3. Also, my Professor told me that some nuclei who aren't "sufficiently unstable" cannot undergo positron decay. Instead they undergo K-electron capture. What is the necessary condition for positron decay? And why does an electron get "captured' by the nucleus? Is there a force/interaction responsible for this?

Answer 1

Why doesn't the emitted positron, while coming out of the nucleus, and passing through the electron cloud annhiliate an electron?

It might, if it happened to scatter on one, but the probability is low, because the electrons are in orbitals around the nucleus, countable, and there is a lot of empty space.

Now, the new nucleus has a proton less and a neutron more. Will the atom still remain electrically neutral? If yes, then the total protons must be equal to the electrons, since one proton is reduced in the interaction, one electron also must reduce, where does this electron go?

The atom will be a negative ion,and depending on the material, (gas, solid , liquid) it will lose an electron to the surroundings.

Also, my Professor told me that some nuclei who aren't "sufficiently unstable" cannot undergo positron decay.

"Sufficiently unstable" means there are lower energy levels for the nucleus, but the energy is not enough to generate a positron. Thus

Instead they undergo K-electron capture. What is the necessary condition for positron decay?

Enough transition between states energy to generate the mass of the positron.

And why does an electron get "captured' by the nucleus? Is there a force/interaction responsible for this?

If you look at the orbitals of electrons, the S ( zero angular momentum) orbitals have a probability of being in the nucleus. Depending on the potentials, their wavefunction will overlap with the wavefunction of a quark within the nuclei, and the weak interaction will allow the capture to happen.