To determine which element would have a full outer shell of electrons if it gained three electrons, we need to consider the electron configurations and the number of valence electrons for each of the elements listed:
A. Argon (Ar) - Argon has 8 valence electrons (full outer shell). Gaining three electrons would give it 11 valence electrons, which is unnecessary.
B. Nitrogen (N) - Nitrogen has 5 valence electrons. If it gains three more electrons, it would have 8 valence electrons, which would fill its outer shell.
C. Boron (B) - Boron has 3 valence electrons. Gaining three electrons would give it 6 valence electrons, which is not a full outer shell.
D. Lithium (Li) - Lithium has 1 valence electron. Gaining three electrons would give it 4 valence electrons, which is not a full outer shell.
The only element that would have a full outer shell if it gained three electrons is B. nitrogen.