The reason atoms with full shells have higher ionization energy than atoms with half-filled shells is due to the concept of electron stability and the underlying principles of quantum mechanics.
In an atom, electrons occupy different energy levels or shells. These energy levels can accommodate a certain maximum number of electrons. According to the Aufbau principle, electrons fill the lowest available energy levels first before moving to higher energy levels. When an energy level is completely filled, the atom is considered to have a stable electronic configuration.
Atoms with full electron shells have achieved a stable configuration, known as the noble gas configuration. In this configuration, the outermost shell is completely filled, and the atom has a high degree of electron stability. These atoms are less likely to lose or gain electrons because doing so would require breaking the stable configuration.
On the other hand, atoms with half-filled shells have a relatively less stable configuration. Their electron arrangements are not as stable as the noble gas configuration. These atoms are more likely to lose or gain electrons to achieve a stable configuration. Consequently, they have a lower ionization energy because it is relatively easier to remove or add an electron to achieve a more stable electron arrangement.
The stability of electron configurations is influenced by factors such as electron-electron repulsion, electron-nucleus attraction, and the arrangement of electrons in different orbitals. The specific energy levels, subshells, and electron configurations determine the overall stability and ionization energy of an atom.