Question

Why a nucleus can eject electrons (β particles) though it contains no electrons?

Answer 1

The answer to this is very simple.
Understand , a beta particle does not come from the electrons in the different shells of the atom but it is formed due to the disintegration of a neuron (in the nucleus of the atom) into protons and electrons. This electron disintegrated out from the neuron is the beta particle.
Thus , you can observe beta emissions from an atom with no electrons but u definitely cannot see a beta emission without the presence of a single nucleus in the atom.