Final answer:
According to the VSEPR model, the molecular geometry of the central carbon atom in CH4 is tetrahedral, with four electron pairs spread out to minimize repulsion, creating equal bond angles of 109.5°.
Step-by-step explanation:
Using the VSEPR model, the molecular geometry of the central atom in CH4, which is carbon, is tetrahedral. When examining its Lewis structure, we can see that carbon contributes four valence electrons, and each hydrogen atom contributes one, adding up to a total of four bonding electron pairs around the carbon atom.
According to VSEPR theory, these electron groups repulse each other and spread out in the most energetically favorable configuration, which is a tetrahedral arrangement with bond angles of 109.5°. This minimizes the repulsion between the electron pairs, leading to a symmetrical, three-dimensional shape where all bond lengths and angles are equal.