The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

Nucleophilic substitution in aromatic compounds is feasible in substrates bearing strong electron-withdrawing substituents positioned ortho or para to the leaving group. The reaction proceeds via two steps: the addition of the nucleophile and the elimination of the leaving group.
The reaction begins with an attack of the nucleophile on the carbon that holds the leaving group. This results in the delocalization of the π electrons over the ring carbons. The resonance interaction between the...

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...