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What is alpha, beta, gamma decay? Give examples?

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Answer
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Hint: Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. Alpha, beta and gamma decays are three most common types of decays, these decays involve emitting one or more particles or photons.

Complete answer:
Alpha decay:- Alpha decay or \[\alpha \]-decay is the type of decay in which the nucleus of the atom emits an alpha particle and transforms or decays into a new atomic nucleus. An alpha particle is a particle with mass number \[4\] and atomic number \[2\], so when the atomic nucleus emits an alpha particle the mass number of the newly formed atom is reduced by \[4\] and atomic number decreases by \[2\].
Equation for alpha decay:
\[_{\text{z}}^{\text{A}}{\text{X}} \to _{{\text{Z - 2}}}^{{\text{A}} - 4}{\text{Y}} + _2^4{\text{He}}\]
Where, \[_{\text{z}}^{\text{A}}{\text{X}}\] is the parent atom, \[_{{\text{Z - 2}}}^{{\text{A}} - 4}{\text{Y}}\] is the newly formed atom and \[_2^4{\text{He}}\] is the alpha particle or helium.
For example,
\[_{92}^{238}{\text{Ur}} \to _{90}^{234}{\text{Th}} + _2^4{\text{He}}\]
Where, \[_{92}^{238}{\text{Ur}}\] is the parent atom, \[_{90}^{234}{\text{Th}}\] is the newly formed atom and \[_2^4{\text{He}}\] is the alpha particle or helium.
Beta decay:- Beta decay is the type of decay in which a proton is transformed into a neutron or a neutron is transformed into a proton inside the nucleus of a radioactive element. In this decay the nucleus emits a beta particle which can be either an electron or positron. There are two types of beta decays, namely \[{\beta ^ - }\]decay and \[{\beta ^ + }\]decay.
In \[{\beta ^ - }\]decay, a neutron is transformed into a proton which causes an increase in atomic number.
\[_{\text{z}}^{\text{A}}{\text{X}} \to _{{\text{Z + 1}}}^{\text{A}}{\text{Y}} + {e^ - } + \overline v \]
Where, \[_{\text{z}}^{\text{A}}{\text{X}}\] is the parent atom, \[_{{\text{Z + 1}}}^{\text{A}}{\text{Y}}\] is the newly formed atom, \[{e^ - }\]is the electron and \[\overline v \] is antineutrino.
In \[{\beta ^ + }\] decay a proton is transformed into a neutron which causes decrease in atomic number.
\[_{\text{z}}^{\text{A}}{\text{X}} \to _{{\text{Z - 1}}}^{\text{A}}{\text{Y}} + {e^ + } + v\]
Where, \[_{\text{z}}^{\text{A}}{\text{X}}\]is the parent atom, \[_{{\text{Z - 1}}}^{\text{A}}{\text{Y}}\] is the newly formed atom, \[{e^ + }\] is the positron and \[v\]is neutrino.
For example,
\[{\beta ^ - }\] decay: A free neutron(\[n\]) decays by \[{\beta ^ - }\] decay into proton (\[p\])
\[n \to p + {e^ - } + \overline v \]
\[{\beta ^ + }\] decay: Decay of a proton (\[p\]) inside the nucleus to a neutron (\[n\])
\[p \to n + {e^ + } + v\]
Gamma decay: Gamma decay is the emission of electromagnetic radiation when a nucleus from higher energy goes down to lower energy giving out the excess amount of energy through the emission of high energy photons.
For example:
\[_{56}^{137}{\text{Ba}} \to _{56}^{137}{\text{Ba}} + \gamma \]
In this example the higher energy parent \[_{56}^{137}{\text{Ba}}\] goes down to lower energy emitting a photon (\[\gamma \]).

Note:The nucleus of an atom is held together by the constant balance between attractive and repulsive electrostatic forces. Since higher mass in the nucleus disturbs the balance between the two electrostatic forces, so the size of the nucleus increases the changes of instability increases. Heavy nuclei of atoms such as Uranium, Polonium are much prone to radioactivity.