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Thus a prism of 1 Δ would produce 1 cm visible displacement at 100 cm, or 1 meter. This can be represented mathematically as: = where is the amount of prism correction in prism dioptres, and is the angle of deviation of the light.
The equation that they developed is as follows: K − 1 = A ε HG − [ H ] 0 − [ G ] 0 + C H C G A ε HG {\displaystyle K^{-1}={\frac {A}{\varepsilon _{\ce {HG}}}}-[{\ce {H}}]_{0}-[{\ce {G}}]_{0}+{\frac {C_{\ce {H}}C_{\ce {G}}}{A}}\varepsilon _{\ce {HG}}}
It is often referred to, incorrectly, as a formula for particle size measurement or analysis. It is named after Paul Scherrer. It is used in the determination of size of crystals in the form of powder. The Scherrer equation can be written as: = where:
Introduction to the concept. Quantum tunnelling falls under the domain of quantum mechanics. To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Quantum mechanics and classical mechanics differ in their treatment of this scenario.
The Davies equation is an empirical extension of Debye–Hückel theory which can be used to calculate activity coefficients of electrolyte solutions at relatively high concentrations at 25 °C. The equation, originally published in 1938, was refined by fitting to experimental data.
The above equation is usually rearranged to yield the following equation for the ease of analysis: p / p 0 v [ 1 − ( p / p 0 ) ] = c − 1 v m c ( p p 0 ) + 1 v m c , ( 1 ) {\displaystyle {\frac {{p}/{p_{0}}}{v\left[1-\left({p}/{p_{0}}\right)\right]}}={\frac {c-1}{v_{\mathrm {m} }c}}\left({\frac {p}{p_{0}}}\right)+{\frac {1}{v_{m}c}},\qquad (1)}
The Eyring equation (occasionally also known as Eyring–Polanyi equation) is an equation used in chemical kinetics to describe changes in the rate of a chemical reaction against temperature. It was developed almost simultaneously in 1935 by Henry Eyring, Meredith Gwynne Evans and Michael Polanyi.
Using the same chemical equation again, write the corresponding matrix equation: s 1 CH 4 + s 2 O 2 s 3 CO 2 + s 4 H 2 O {\displaystyle {\ce {{\mathit {s}}_{1}{CH4}+{\mathit {s}}_{2}{O2}->{\mathit {s}}_{3}{CO2}+{\mathit {s}}_{4}{H2O}}}}
For momentum = ˙, = ˙ and their ratio = the equation of motion is (see Binet equation) d 2 u d φ 2 = − ( 1 − k 2 Z 2 e 4 c 2 p φ 2 ) u + m 0 k Z e 2 p φ 2 ( 1 + W m 0 c 2 ) = − ω 0 2 u + K {\displaystyle {\frac {d^{2}u}{d\varphi ^{2}}}=-\left(1-k^{2}{\frac {Z^{2}e^{4}}{c^{2}p_{\mathrm {\varphi } }^{2}}}\right)u+{\frac {m_{\mathrm {0 ...
From the previous two equations, and with the appropriate boundary conditions, for a far-field uniform-flow velocity u in the z –direction and a sphere of radius R, the solution is found to be ψ ( r , z ) = − 1 2 u r 2 [ 1 − 3 2 R r 2 + z 2 + 1 2 ( R r 2 + z 2 ) 3 ] . {\displaystyle \psi (r,z)=-{\frac {1}{2}}\,u\,r^{2}\,\left[1-{\frac {3 ...