Answer
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The claim that subshells half-filled with electrons are particularly stable is based on the concept of electron-electron repulsion. When electrons are added to an atom or ion, they repel each other due to their negative charges. This repulsion can be minimized by arranging the electrons in a way that achieves the most stable electron configuration.
Half-filled subshells have electrons with parallel spins, following Hund's rule. In this configuration, the electrons are maximally spread out in the subshell, minimizing their mutual repulsion. This arrangement leads to greater stability and lower energy compared to other configurations.