Which of the following statements best explains the shapes of atomic orbitals according to molecular orbital theory?

• A. The shapes of atomic orbitals are determined by the mathematical solutions to the Schrödinger equation for electrons in atoms.
• B. The shapes of atomic orbitals are determined by the type of chemical bonds formed.
• C. The shapes of atomic orbitals are defined by the number of protons in the nucleus.
• D. The shapes of atomic orbitals are a result of the arrangement of atoms in a molecule.

Answer: (A)

Verified step by step guidance

1. Understand that atomic orbitals are regions in space where there is a high probability of finding an electron around an atom.
2. Recall that molecular orbital theory is based on quantum mechanics, specifically the Schr\"odinger equation, which describes how electrons behave in atoms and molecules.
3. Recognize that the shapes of atomic orbitals arise from the mathematical solutions to the Schr\"odinger equation for electrons in atoms, which produce wavefunctions (orbitals) with specific shapes and energies.
4. Note that the other options (chemical bonds, number of protons, arrangement of atoms) influence molecular properties but do not directly determine the fundamental shapes of atomic orbitals.
5. Conclude that the best explanation is that the shapes of atomic orbitals come from the quantum mechanical solutions to the Schr\"odinger equation.