Final answer:
The shape of an ammonium ion (NH4+) is most similar to methane (CH4) because both display a tetrahedral electron-pair geometry and molecular structure.
Step-by-step explanation:
According to the VSEPR theory, the shape of an ammonium ion (NH4+) is most similar to that of methane (CH4). This is because both NH4+ and CH4 have a central atom with four bonding electron pairs and no lone pairs, resulting in a tetrahedral electron-pair geometry and a tetrahedral molecular structure. In comparison, BH3 has a trigonal planar shape, and N2 is a diatomic molecule with a linear shape, making them quite different from NH4+.