Radioactivity is a/an ...... process.

$A$ nuclear reaction given by $_Z{X^A} \to {_{Z+1}}{Y^A} + _{-1}{e^0} + \bar{\nu}$ represents:

$A$ nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If $M(A, Z)$ denotes the mass of a single neutral atom of an element with mass number $A$ and atomic number $Z$,then the minimal condition that the $\beta^{-}$ decay $X_Z^A \rightarrow Y_{Z+1}^A + \beta^{-} + \bar{\nu}_e$ will occur is ($m_e$ denotes the mass of the $\beta^{-}$ particle and the neutrino mass $m_{\nu}$ can be neglected).

In the given nuclear decay process,identify the order in which radioactive radiations are emitted:
${}_{Z}^{A}X \to {}_{Z+1}^{A}Y \to {}_{Z-1}^{A-4}K \to {}_{Z-1}^{A-4}K$

Assertion: ${}_{Z}{X^{A}}$ undergoes $2\alpha$-decays,$2\beta$-decays,and $2\gamma$-decays,and the daughter product is ${}_{Z-2}{X^{A-8}}$.
Reason: In $\alpha$-decays,the mass number decreases by $4$ and the atomic number decreases by $2$. In $\beta$-decays,the mass number remains unchanged,but the atomic number increases by $1$.

$A$ radioactive nucleus is initially at rest. It decays by emitting an electron and a neutrino at right angles to each other. The momentum of the electron is $3.2 \times 10^{-23} \ kg \cdot m/s$ and the momentum of the neutrino is $6.4 \times 10^{-23} \ kg \cdot m/s$. What is the direction of the recoil of the nucleus with respect to the direction of the electron?