Which of the following statements about hybrid orbitals is or are true? (i) After an atom undergoes sp hybridization, there is one unhybridized \(p\) orbital on the atom, (ii) Under \(s p^{2}\) hybridization, the large lobes point to the vertices of an equilateral triangle, and (iii) The angle between the large lobes of \(s p^{3}\) hybrids is \(109.5^{\circ} .\)

When we delve into the concept of sp hybridization, it unveils a fascinating aspect of chemical bonding where one s and one p orbital merge to form two equivalent orbitals known as sp hybrids. This process is akin to reshuffling a deck of cards to create a new hand, with the goal to allow atoms to form stronger covalent bonds.

Visualize the sp hybrid orbitals as two vast lobes extending in opposite directions, forming a linear geometry with a bond angle of 180°. It's essential to highlight a common misunderstanding — after undergoing sp hybridization, an atom will possess not one, but two unhybridized p orbitals. These remaining p orbitals are available for further bonding such as pi bonds in multiple-bonded systems like ethyne, commonly referred to as acetylene.

Now, let us turn to sp2 hybridization. This is where the dance of electrons comes into play with one s and two p orbitals getting into the groove. By assimilating and rebalancing themselves, they form three equivalent sp2 hybrid orbitals.

The result is a molecule flaunting a flat, triangular layout, also known as trigonal planar, with each bond making a 120° angle with its neighbors. The geometry is as symmetrical as the points of an equilateral triangle, optimizing the distribution of electron clouds and thus stabilizing the molecule. This form of hybridization is a key player in structures like ethene (ethylene), showcasing a double bond structure with a sigma and pi bond.

Moving over to sp3 hybridization, we witness an atom extending its bonding reach even further. By combining one s and three p orbitals, it gives rise to four sp3 hybrid orbitals, each equally adept at forming covalent bonds.

The orbited molecules take on a tetrahedral structure, resembling a pyramid with a triangular base. Within this geometric arrangement, the bond angles are precisely 109.5°, striking a perfect balance that minimizes electron repulsion. This tetrahedral model forms the backbone of many organic molecules, including ethane and methane, reinforcing the foundations of organic chemistry.

The term orbital geometry refers to the spatial arrangement of the hybrid orbitals around a central atom. It's the spatial consideration of where these newly mixed 'hands' of electrons are placed for maximum efficiency and minimal repulsion.

The directional attributes of hybrid orbitals give us clues to how atoms bond and the shape molecules adopt. Whether it's the 180° apart hands of sp hybridization, the 120° spaced arms of sp2 hybridization, or the four corners of a tetrahedron in sp3 hybridization, the blueprint of each tells a tale of molecular architecture that dictates the physical and chemical properties of the substance.

Molecular geometry, unlike orbital geometry, is concerned with the arrangement of the actual atoms in a molecule. Picture it as the framework that results when the bones (orbitals) come together, determined by the vertices where the atoms reside, and the flesh (electron pairs) fill out the structure.

Atoms bonded through sp3 hybridization form a tetrahedral molecular geometry, yet if there are lone pairs involved, the geometry transforms — creating bent or trigonal pyramidal shapes instead. These forms are central to understanding why water is a polar molecule and why ammonia has a distinct odor. They're the sculptors of molecules, carving out the final form that defines function.