## Highlights Of The Chapter

• Both light and matter simultaneously exhibit dual characters as waves and particles.

• Light as particles consists of photons of discrete energy values, a condition called quantization of energy.

• As photons, light exchanges energy and momentum with matter. Energy exchange forms the basis for spectroscopy, while momentum exchange provides physical effects—for example, optical force for trapping of matter.

• As a wave, light behaves as an electromagnetic wave, which consists of electric and magnetic oscillations perpendicular to each other as well as perpendicular to the direction of propagation.

• As a wave, light is characterized by a length, called the wavelength, which is the distance between two successive peaks of a wave.

• As waves, light exhibits the phenomena of interference between electromagnetic waves and diffraction at an aperture or a slit.

• The speed of light in a medium is reduced compared to its propagation in a vacuum by a factor called the refractive index.

• The refractive index of a medium typically decreases with increasing wavelength, as in going from the blue end to the red end of the visible range.

• A wave packet of light is called coherent if all the waves superimpose with their peaks and troughs on top of each other. This is the case for laser light.

• Polarization of light refers to an orientation of the oscillation of electric field of light.

• An optically active medium rotates the plane of polarization of light, while a birefringent medium exhibits different refractive index and, thus, different propagation speed for different polarization of incident light.

• Quantum conditions for the energy states of a matter are derived from the solution of the Schrodinger equation.

• The Heisenberg uncertainty principle places the restriction that the simultaneous knowledge of the exact position of a particle (e.g., an electron) and its velocity cannot be known, necessitating a probabilistic description of the spatial distribution of an electron's position.

• This probabilistic description is provided by the square of a wave function, which is also the solution of Schrodinger equation.

• The energy levels of electrons in an atom are quantized; that is, they can only have certain discrete values.

• Each electronic energy level of an atom is represented by an atomic orbital, which is the region of space where the probability of finding an electron is high.

• A molecule exhibits four types of energies: electronic, vibrational, rotational, and translational; of these, only electronic, vibrational, and rotational levels exhibit quantization effects (possess discrete values).

• The electronic states of a molecule are obtained by using the molecular orbital (MO) approach, which involves the overlap of atomic orbitals of the atoms forming a bond.

• A constructive overlap of atomic orbitals, just like a constructive interference between waves, forms a bonding MO; a destructive overlap produces antibonding MO.

• Overlap of atomic orbitals along the intermolecular axis produces a o bond, while a lateral overlap produces a p bond.

• Carbon atoms can form multiple bonds, such as double and triple bonds. Of the multiple bonds between two carbon atoms, the first is a o bond; the others are p bonds.

• Conjugated organic structures contain alternating single and multiple bonds between a chain of carbon atoms.

• The behavior of molecular orbitals and other energy states of a molecule is determined by the symmetry elements of the molecule, which together define its symmetry point group.

• The vibrational energy states of a molecule are described in the harmonic oscillator model. A molecule possesses a minimum energy called zero-point energy.

• A molecule exhibits a number of vibrational displacement patterns called normal modes, but often the vibrations are described as being associated with the displacement of a bond or deformation of an angle.

• Intermolecular interactions among molecules profoundly affect the electronic, vibrational, and rotational energy levels.

• The three-dimensional arrangement of bonded atoms in a molecule determines its shape and also gives rise to stereoisomers that have the same chemical formula and bonding but different spatial arrangements.

• Geometrical isomers are generally stereoisomers of a molecule containing a double bond. The cis isomer has two identical atoms (or groups) on the same side of the double bonds; the trans isomer has them on the opposite sides.

• Optical isomers or enantiomers have three-dimensional structures that are mirror images of each other.

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