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The CRC Handbook of Chemistry and Physics defines specific rotation as: For an optically active substance, defined by [α] θ λ = α/γl, where α is the angle through which plane polarized light is rotated by a solution of mass concentration γ and path length l. Here θ is the Celsius temperature and λ the wavelength of the light at which ...
Sucrose is particularly dangerous as a risk factor for tooth decay because Streptococcus mutans bacteria convert it into a sticky, extracellular, dextran-based polysaccharide that allows them to cohere, forming plaque. Sucrose is the only sugar that bacteria can use to form this sticky polysaccharide.
The purity of a quantum state is conserved under unitary transformations acting on the density matrix in the form †, where U is a unitary matrix. Specifically, it is conserved under the time evolution operator U ( t , t 0 ) = e − i ℏ H ( t − t 0 ) {\displaystyle U(t,t_{0})=e^{{\frac {-i}{\hbar }}H(t-t_{0})}\,} , where H is the ...
The refining process completely removes the molasses from cane juice or beet juice to give the disaccharide white sugar, sucrose. It has a purity higher than 99.7%. [1] Its molecular formula is C 12 H 22 O 11. [2]
The ratio, the purity, and the concentration of two enantiomers can be measured via polarimetry. Enantiomers are characterized by their property to rotate the plane of linear polarized light. Therefore, those compounds are called optically active and their property is referred to as optical rotation. Light sources such as a light bulb, Tungsten ...
The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region ...
The fidelity between two quantum states and , expressed as density matrices, is commonly defined as: [1] [2] (,) = ().The square roots in this expression are well-defined because both and are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem.
For a pure substance in solution, if the color and path length are fixed and the specific rotation is known, the observed rotation can be used to calculate the concentration. This usage makes a polarimeter a tool of great importance to those trading in or using sugar syrups in bulk.