Identify the parent nuclides and daughter nuclides in the nuclear equation. Which kind of radioactive decay is involved? $$ { }_{91}^{231} \mathrm{~Pa} \longrightarrow \frac{227}{89} \mathrm{Ac}+{ }_{2}^{4} \mathrm{He} $$

In the world of nuclear chemistry, a \textbf{parent nuclide} refers to the original, unstable atom that initiates the process of radioactive decay. It's like the 'parent' in a family who passes on traits to its 'children'. In our nuclear equation, \( _{91}^{231}\text{Pa} \) serves this role. Think of this parent as an overfilled suitcase, bulging at the seams and longing to let out some items to reach a more stable state.

To further clarify, the atomic number (91 in this case) tells us this suitcase is packed with 91 protons, and the mass number (231) adds together the total number of protons and neutrons. It's key in identifying which element we are dealing with—here, it's Protactinium (Pa).

After the parent nuclide has let go of its excess, we are left with a \textbf{daughter nuclide}, which essentially is the 'offspring' of the original atom post-decay. In our example, the daughter is \( _{89}^{227}\text{Ac} \). This newly formed nuclide exhibits more stability than its parent and has its own distinct set of properties, including a different number of protons which defines a new element—Actinium (Ac).

The change from parent to daughter is like handing down old clothes to a sibling; the core wardrobe (nuclide structure) remains, but a few items (particles) are removed, altering the look (elemental identity) significantly. This transformation is central to understanding the process of radioactive decay.

Among the various types of radioactive decay, our exercise features \textbf{alpha decay}, which is a bit like a heavy fruit falling off a tree due to its weight. In alpha decay, the parent nuclide releases an alpha particle—a tiny packet consisting of 2 protons and 2 neutrons, exactly the composition of a helium nucleus, \( _{2}^{4}\text{He} \).

This release is the suitcase (parent nuclide) popping open and letting go of a small pouch (alpha particle) to achieve comfort. Importantly, because 2 protons are lost, the identity of the original atom shifts, becoming a completely different element. This decay mode is significant in elements with heavy, packed nuclei, nudging them closer to stability.

The \textbf{nuclear equation} is a succinct way to illustrate the changes happening during radioactive decay. Just like a mathematical equation balances both sides, a nuclear equation ensures that the total number of protons and neutrons remains constant. In the provided nuclear reaction:
\[ _{91}^{231}\text{Pa} \longrightarrow _{89}^{227}\text{Ac} + _{2}^{4}\text{He} \]
the sum of the protons (the bottom number) and the sum of the mass numbers (the top number) before and after decay are equal. This shows the law of conservation of mass and charge in action. The equation capably summarizes the entire drama of decay: the initial act (parent nuclide), the cast-off (alpha particle), and the final outcome (daughter nuclide).