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Related Concept Videos

Chirality02:25

Chirality

27.0K
Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
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Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

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Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
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Chirality at Nitrogen, Phosphorus, and Sulfur02:30

Chirality at Nitrogen, Phosphorus, and Sulfur

6.2K
Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...
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Chirality in Nature02:30

Chirality in Nature

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Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid.
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Molecules with Multiple Chiral Centers02:25

Molecules with Multiple Chiral Centers

13.7K
Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...
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Related Experiment Video

Updated: Oct 17, 2025

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
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Scattering by a chiral sphere above a half-space.

Hasan Zamani

    Optics Express
    |October 7, 2021
    PubMed
    Summary

    This study analytically examines scattering from a chiral sphere over a lossy half-space, crucial for remote sensing and optics. The findings offer a new method for calculating scattered fields in complex electromagnetic environments.

    Area of Science:

    • Electromagnetics and Optics
    • Computational Physics
    • Remote Sensing

    Background:

    • Chiral spheres and lossy half-spaces are relevant in various optical and remote sensing applications.
    • Analytical solutions for scattering problems involving complex geometries and materials are computationally challenging.

    Purpose of the Study:

    • To develop an analytical method for calculating electromagnetic scattering from a chiral sphere situated above a lossy half-space.
    • To combine vector Mie solutions with plane wave transformations for a comprehensive scattering analysis.

    Main Methods:

    • The study employs a hybrid approach, integrating the vector Mie solution for the chiral sphere with field transformations between vector spherical functions (VSFs) and plane waves (PWs).
    • It utilizes reflection coefficients of the lossy half-space and derives Mie fields for successive orders, converting the series solution to a non-recursive formulation.

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  • The total scattered field is computed as the sum of the direct Mie field and its reflection from the underlying half-space.

    • Main Results:

    • An analytical expression for the total scattered field is derived.
    • The method provides a non-recursive formulation for the Mie field, enhancing computational efficiency.
    • Numerical validation confirms the accuracy of the derived expressions for various scenarios.

    Conclusions:

    • The developed analytical method accurately models scattering from a chiral sphere above a lossy half-space.
    • This approach offers a valuable tool for electromagnetic scattering analysis in remote sensing and optical applications.
    • The numerical results provide insights into the behavior of scattered fields under different conditions.