Alpha decay

In alpha decay, an unstable nucleus emits an alpha particle - a $^{4}_{2}He$ nucleus, i.e. two protons and two neutrons bound together. Since the parent loses two protons and two neutrons, its atomic number $Z$ decreases by 2 and its mass number $A$ decreases by 4. The general decay equation is

where $X$ is called the parent nucleus and $Y$ the daughter nucleus. A concrete example is the decay of uranium-238 to thorium-234 with the emission of an alpha particle: ${}^{238}_{92}U\to{}^{234}_{90}Th+{}^{4}_{2}He$.

Why a whole $^{4}_{2}He$ nucleus, and not four separate nucleons? The answer is energy conservation. The mass of $^{4}_{2}He$ is significantly less than the combined mass of two free protons plus two free neutrons (because the alpha particle itself has a large internal binding energy), so emitting it as one bound unit releases a positive disintegration energy $Q$. If the same uranium nucleus instead tried to emit four separate, unbound nucleons, the total mass of the products would actually turn out to be greater than the parent's mass - meaning $Q$ would be negative, which would violate conservation of energy and simply cannot happen spontaneously in nature.

Disintegration energy. The mass difference between parent and products, $\Delta m=m_X-(m_Y+m_\alpha)$, is released as the disintegration energy

$Q=[m_X-m_Y-m_\alpha]c^2\qquad (8.27)$ …