Explain the $\alpha$-decay process and give its appropriate example.

(N/A) In the $\alpha$-decay phenomenon,an unstable nucleus spontaneously transforms into a new nucleus by emitting an $\alpha$-particle.
An $\alpha$-particle is the nucleus of a helium atom,represented as ${ }_{2}^{4} He$.
The decaying nucleus is called the parent nucleus,and the newly formed nucleus is called the daughter nucleus.
In $\alpha$-decay,the mass number of the daughter nucleus is $4$ less than that of the parent nucleus,while the atomic number decreases by $2$.
The general equation for $\alpha$-decay is:
${ }_{Z}^{A} X \rightarrow{ }_{Z-2}^{A-4} Y+{ }_{2}^{4} He+Q$
Where $X$ is the parent nucleus,$Y$ is the daughter nucleus,and $Q$ is the total kinetic energy released,calculated using Einstein's mass-energy equivalence:
$Q = [m_{X} - m_{Y} - m_{He}] c^{2}$
Here,$m_{X}$ is the mass of the parent nucleus,$m_{Y}$ is the mass of the daughter nucleus,$m_{He}$ is the mass of the $\alpha$-particle,and $c$ is the speed of light in a vacuum.
If the original nucleus is at rest,$Q$ represents the kinetic energy of the products. If $Q > 0$,the process is exothermic; if $Q < 0$,it is endothermic.
Example: The decay of Uranium-$238$ into Thorium-$234$ with the emission of an $\alpha$-particle:
${ }_{92}^{238} U \rightarrow{ }_{90}^{234} Th+{ }_{2}^{4} He + Q$