Explain $\beta$-decay and how a radioactive nucleus emits $\beta$-particles,even if there are no $\beta$-particles in the nucleus. Why does the mass number of the radioactive nuclide not change during $\beta$-emission?

(N/A) The process in which a nucleus spontaneously emits an electron ($\beta^{-}$-decay) or a positron ($\beta^{+}$-decay) is called $\beta$-decay.
$\beta$-decay is a spontaneous process characterized by a specific disintegration energy and half-life $(T_{1/2})$,following the laws of radioactive decay.
In $\beta^{-}$-decay,the emission of an electron is accompanied by the emission of an antineutrino $(\bar{\nu})$,while in $\beta^{+}$-decay,a positron is emitted along with a neutrino $(\nu)$.
Neutrinos have negligible mass and interact only weakly with matter,making them extremely difficult to detect.
In $\beta^{-}$-decay,a neutron inside the nucleus transforms into a proton,an electron,and an antineutrino: $n \rightarrow p + e^{-} + \bar{\nu}$.
The general equation for $\beta^{-}$-decay is: ${ }_{Z}^{A} X \rightarrow{ }_{Z+1}^{A} Y+{ }_{-1}^{0} e+\bar{\nu}$.
Since a neutron is converted into a proton,the total number of nucleons $(A = Z + N)$ remains constant. Because the mass of a proton and a neutron are nearly equal,the mass number of the nuclide does not change during $\beta$-emission.