What mode of decay would convert Mg-20, 21, 22, and 23 into stable isotopes most quickly?

In the context of nuclear decay and stability, the key to understanding why electron capture is the most effective mode for transforming isotopes of magnesium (Mg-20, Mg-21, Mg-22, and Mg-23) into stable forms lies in the nature of each isotope and how they interact with their surroundings.

Electron capture occurs when an electron from the innermost energy level is captured by the nucleus, combining with a proton to form a neutron. This process effectively reduces the atomic number of the atom, which can lead to the formation of a more stable isotope, especially when dealing with isotopes that have excess protons—common in lighter elements like magnesium. For isotopes that are close to or above the line of stability, this decay mode can directly convert them into isotopes that are more stable or even naturally occurring stable isotopes.

For magnesium isotopes in particular, those like Mg-21 have a higher proton-to-neutron ratio, making them less stable. Electron capture is particularly efficient because it directly addresses the imbalance by reducing the number of protons, thereby fostering stability.

The other decay modes, while they may lead to stability over time, do not typically target the proton-to-neutron ratio as effectively in these specific cases. Alpha