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How can I write the nuclear equation for alpha decay?

Answer
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Hint Alpha-decay means there is the removal of an alpha particle from a heavy nucleus which is able to undergo radioactive decay. Alpha particle is mainly a helium atom so, when the alpha particle is removed then there is a decrease in mass number and atomic number in the heavier nucleus equal to the mass number and an atomic number of a helium atom.

Complete step by step answer:
Radioactive decay is a property of a heavier nucleus in which by the removal of certain substances or particles it can convert itself to smaller nuclei and there is the release of a huge amount of energy. Mainly we know three types of decay i.e., alpha-decay, beta-decay, and gamma-decay.
Alpha-decay means there is the removal of an alpha particle from a heavy nucleus which is able to undergo radioactive decay. Alpha particle is mainly a helium atom so, when the alpha particle is removed then there is a decrease in mass number and atomic number in the heavier nucleus equal to the mass number and an atomic number of a helium atom.
So, the helium atom is represented as $_{2}^{4}He$. Therefore, overall in the alpha-decay, there is a decrease in the number of 2 protons and 2 neutrons from the heavy nuclei.
This can be written as:
$_{x}^{y}X\to _{x-2}^{y-4}Y+_{2}^{4}He$
So, in this reaction, an X nucleus undergoes alpha-decay and converts into Y nuclei and release of alpha-particle.
For example, radium will convert into radium, the equation is given below:
$_{88}^{226}Ra\to _{86}^{222}Rn+_{2}^{4}He$

Note: Beta-decay also occurs in the same way, there are two reactions for the beta-decay:
Equation when there is plus beta-decay:
$_{Z}^{A}X\to _{Z-1}^{A}Y+{{e}^{+}}+v$
Equation when there is minus beta-decay
$_{Z}^{A}X\to _{Z+1}^{A}Y+{{e}^{-}}+\bar{v}$