A racemic mixture, or racemate, is an equimolar mixture of enantiomers of a molecule that can be separated using their unique interaction with chiral molecules or media. Racemic mixtures are denoted by the (±)- prefix. This ‘optical rotation descriptor’ applies to the whole solution of a racemic mixture rather than a specific stereoisomer. Enantiomers typically have the same physical and chemical properties. Hence, they are not easily separable. However, enantiomers can exhibit different...

During the 1950s, the landmark Robbers Cave experiment demonstrated that when groups must compete with one another, intergroup conflict, hostility, and even violence may result. At the Oklahoman summer camp, two troops of boys—termed the Rattlers and the Eagles—took part in a week-long tournament. During this time, their negativity culminated in derogatory name-calling, fistfights, and even vandalism and destruction of property. However, this work also revealed that such tension could be...

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The current density that results depends on the electrical field and the properties of the material. In some materials, including metals at a given temperature, the current density is approximately proportional to the electrical field. In these cases, the current density can be modeled as:

Organic compounds of the same molecular formula can have different structural formulas called constitutional isomers, and the phenomenon is known as constitutional isomerism. Alkanes with four or more carbons showing multiple structures with the same molecular formula thereby exhibit constitutional isomerism.
The linear isomer of an alkane is prefixed by the term “n”; hence a linear isomer of pentane is known as n-pentane. Based on the type of branching, some of the branched isomers are given...

Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...