In the $\alpha$-decay phenomenon the unstable nucleus automatically converts and forms a new nucleus and emits $\alpha$-particles.

$\alpha$-particle is the nucleus of helium.

$\therefore \alpha={ }_{2} \mathrm{He}^{4}$

The disintegrating nucleus is called the parent nucleus and the newly formed nucleus is called the daughter nucleus.

In a $\alpha$-decay, the mass number of the product nucleus is four less than that of decaying nucleus

while the atomic number decreases by two.

The equation of $\alpha$-decay can be expressed as follows:

${ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow{ }_{\mathrm{Z}-2}^{\mathrm{A}-4} \mathrm{Y}+{ }_{2}^{4} \mathrm{He}+\mathrm{Q}$

$\text { where } X=\text { parent nucleus }$ $Y=\text { daughter nucleus }$

$Q=$Which is the total kinetic energy released in the process which can be determined from the relation of the mass and energy of the Einstein.

$\mathrm{Q}=\left[m_{\mathrm{X}}-m_{\mathrm{Y}}-m_{\mathrm{He}}\right] c^{2}$

where $m_{\mathrm{X}}=$ mass of parent nucleus

$m_{\mathrm{Y}}=$ mass of daughter nucleus

$m_{\mathrm{He}}=$ mass of $\alpha$-particle and

$c$ speed of light in vacuum

If original nucleus is at rest, $Q$ is the kinetic energy of the products.

As $Q>0$ for $\alpha$-decay, this process is exothermic process as a $Q<0$, this process is endothermic process.

If original nucleus is at rest, $\mathrm{Q}$ is the kinetic energy of the products.

As $\mathrm{Q}>0$ for $\alpha$-decay, this process is exothermic process as a $\mathrm{Q}<0$, this process is endothermic

process.

Example : The decay of ${ }_{92}^{238} \mathrm{U}$ to thorium ${ }_{90}^{234} \mathrm{Th}$ with emission of a helium nucleus ${ }_{2}^{4} \mathrm{He}$

( $\alpha$-particles) whose chemical equation,

${ }_{92}^{238} \mathrm{U} \rightarrow{ }_{90}^{234} \mathrm{~T} h+{ }_{2}^{4} \mathrm{H} e+\mathrm{Q}$

where $\mathrm{Q}$ is the emitted heat,

$\mathrm{Q}=\left[m_{\mathrm{U}}-m_{\mathrm{Th}}-m_{\mathrm{He}}\right] c^{2}$