The molecular shape of the methane molecule CH4 according to the valence shell electron pair repulsion VSEPR theory is tetrahedral. In a methane molecule, the central carbon atom is bonded to four hydrogen atoms. The VSEPR theory states that electron pairs around a central atom will arrange themselves to minimize repulsion between them. In the case of methane, there are four bonding electron pairs, and these pairs arrange themselves in a tetrahedral geometry to minimize repulsion. The bond angle between the hydrogen atoms is approximately 109.5 degrees.From the quantum mechanics point of view, the explanation for the tetrahedral shape of methane involves the hybridization of atomic orbitals. The carbon atom has four valence electrons, which occupy the 2s and 2p orbitals. In the ground state, carbon has the electron configuration 1s2s2p. To form four equivalent bonds with the hydrogen atoms, the 2s and three 2p orbitals of carbon hybridize to form four sp hybrid orbitals. These sp orbitals are equivalent in energy and have a tetrahedral arrangement in space.Each of the four sp hybrid orbitals of carbon overlaps with the 1s orbital of a hydrogen atom, forming four sigma bonds. The resulting CH4 molecule has a tetrahedral shape, with the carbon atom at the center and the four hydrogen atoms surrounding it. This tetrahedral arrangement is a direct consequence of the hybridization of atomic orbitals and the minimization of electron pair repulsion, as described by the VSEPR theory.