Final answer:
Aluminum is a member of group 13 rather than group 3 due to its valence electron configuration, the formation of a +3 cation, and its atomic number.
Step-by-step explanation:
The electron configuration of Al atom is 1s²2s²2p63s²3p¹. Aluminum has three valence electrons in the third energy level, (3s²3p¹). The cation, Al³+, is formed when these three valence electrons are lost, leaving the configuration for the noble gas neon, 1s²2s²2p6.
For groups 13-17, the group numbers exceed the number of valence electrons by 10 (accounting for the possibility of full d subshells in atoms of elements in the fourth and greater periods).
Thus, the charge of a cation formed by the loss of all valence electrons is equal to the group number minus 10. For example, aluminum (in group 13) forms 3+ ions (Al³+).
The number of protons remains unchanged when an atom forms an ion, so the atomic number of the element must be 13. Aluminum has lost three electrons and has three more positive charges (13) than it has electrons (10). This is the aluminum cation, Al³+.
However, the first ionization energy decreases at Al ([Ne]3s²3p¹) and at S ([Ne]3s²3p4). The electrons in aluminum's filled 3s² subshell are better at screening the 3p¹ electron than they are at screening each other from the nuclear charge, so the s electrons penetrate closer to the nucleus than the p electron does and the p electron is more easily removed.