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The radial distance ρ is the Euclidean distance from the z-axis to the point P. The azimuth φ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of P on the plane. The axial coordinate or height z is the signed distance from the chosen plane to the point P.
The physics convention. Spherical coordinates (r, θ, φ) as commonly used: (ISO 80000-2:2019): radial distance r (slant distance to origin), polar angle θ (angle with respect to positive polar axis), and azimuthal angle φ (angle of rotation from the initial meridian plane). This is the convention followed in this article.
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
The Bohr radius ( ) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.291 772 105 44 (82) × 10 −11 m. [1] [2]
Radial distance, typically denoted r or ρ , is the distance from the origin to a point along the radial dimension in a: Polar coordinate system Spherical coordinate system
In the general time-independent case, the dynamics of a particle in a spherically symmetric potential are governed by a Hamiltonian of the following form: ^ = ^ + Here, is the mass of the particle, ^ is the momentum operator, and the potential () depends only on the vector magnitude of the position vector, that is, the radial distance from the ...
calculation of () Radial distribution function for the Lennard-Jones model fluid at =, =.. In statistical mechanics, the radial distribution function, (or pair correlation function) () in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle.
The LeRoy radius, derived by Robert J. LeRoy, defines the internuclear distance between two atoms at which LeRoy-Bernstein theory (sometimes called near-dissociation theory) becomes valid. LeRoy-Bernstein theory is a semi-classical ( WKB ) approach for describing vibrational energy levels near the molecular dissociation limit. [ 1 ]