In a beam of charged particles created by a heated cathode, the particles move at different speeds. However, many applications need a beam with uniform particle speeds. An arrangement known as a velocity selector uses electric and magnetic fields to pick particles with a particular speed from the beam.
A particle with charge q, speed v, and mass m enters an area from the top, where the magnetic and electric fields are perpendicular both to the particle's motion and to one another. The magnetic...

Polydentate ligands are most widely used in complexometric titrations because they form more stable complexes with the metal ions than mono- or bidentate ligands due to the chelate effect. Examples of polydentate ligands are ethylenediaminetetraacetic acid (EDTA), crown ethers, and cryptands. The most important feature of optimal polydentate ligands is the ability to form 1:1 complexes in a single-step process. Amino carboxylic acid derivatives are frequently used as complexing agents. EDTA is...

A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...

The EDTA titration types for metal ion analysis include direct titration, back-titration, and replacement titration.
Direct titration involves buffering the metal ion solution to the desired pH and directly titrating with standard EDTA until the endpoint. The optimum pH ensures a large conditional formation constant of metal−EDTA and visibility of the free indicator color in the solution. In addition, auxiliary complexing reagents are used to prevent the precipitation of metal hydroxides and...

Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward force was unique to Earth. By the 16th century, Nicolaus Copernicus (1473-1543) put forward the heliocentric theory, which suggested that Earth and other planets orbited the sun, while the Moon orbited the Earth. However, it was Isaac Newton (1642-1727) who linked these two motions together in the 17th century. He reasoned that the force of...