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The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis.
Linearity. The Schrödinger equation is a linear differential equation, meaning that if two state vectors and are solutions, then so is any linear combination. of the two state vectors where a and b are any complex numbers. [13] : 25 Moreover, the sum can be extended for any number of state vectors.
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.
In this case, a correction factor in the numerator is necessary:: 248 : 123 [ α ] λ T = 100 × α l × c {\displaystyle [\alpha ]_{\lambda }^{T}={\frac {100\times \alpha }{l\times c}}} When using this equation, the concentration and the solvent may be provided in parentheses after the rotation.
Planck's law describes the unique and characteristic spectral distribution for electromagnetic radiation in thermodynamic equilibrium, when there is no net flow of matter or energy. [2] Its physics is most easily understood by considering the radiation in a cavity with rigid opaque walls.
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.
The formula for Volume Correction Factor is commonly defined as: V C F = C T L = exp { − α T Δ T [ 1 + 0.8 α T ( Δ T + δ T ) ] } {\displaystyle VCF=C_{TL}=\exp\{-\alpha _{T}\Delta T[1+0.8\alpha _{T}(\Delta T+\delta _{T})]\}}
Antoine equation. The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented in 1888 by the French engineer Louis Charles Antoine [ fr] (1825–1897).
The formula for the interaction is Φ 12 ( r ) = A exp ( − B r ) − C r 6 + q 1 q 2 4 π ε 0 r {\displaystyle \Phi _{12}(r)=A\exp \left(-Br\right)-{\frac {C}{r^{6}}}+{\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r}}}
This equation is formally similar to the particle diffusion equation, which one obtains through the following transformation: c ( R , t ) → ψ ( R , t ) D → i ℏ 2 m {\displaystyle {\begin{aligned}c(\mathbf {R} ,t)&\to \psi (\mathbf {R} ,t)\\D&\to {\frac {i\hbar }{2m}}\end{aligned}}}