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Sodium has one unpaired electron in the 3s subshell, thus it is more inclined to lose that electron. If it loses that electron to an electronegative atom like chlorine the subshells are "satisfied" because the valence electrons are balanced in a "full" subshell. Aluminum requires more energy because it has an unpaired electron in the 3p subshell and it is less likely to lose that electron.
The atomic radius of Aluminum is smaller than that of Sodium. Therefore, the outer electrons of an Aluminum atom are closer to the nucleus, and thus are more strongly attracted to the nucleus than are Sodium's electrons.
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