Question

There is no electron in the nucleus of an atom. how then the beta particles are emitted from the nucleus of an atom?

Answer 1

In radioactive emissions of beta particles (energetic electrons), a bound neutron in the nucleus changes into a proton inside the nucleus, with the emission of a electron and an anti-neutrino.

Since mass of a free neutron is more than that of a free proton, a free neutron also decays in a similar fashion, i.e into a proton, electron, and anti-neutrino.

A bound proton also changes into a neutron with the emission of a positron, and a neutrino. It needs to be emphasized that only a bound proton inside the nucleus, undergoes this conversion i.e. into a neutron, a positron, and a neutrino.

So although, electrons (positrons) are not present in the nucleus, these are spontaneously created at the time of decay and are emitted.