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Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

The Dot Product

The Dot Product

Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...

Dot Product

Dot Product

The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...

Dot Product: Problem Solving

Dot Product: Problem Solving

The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them measured anti-clockwise. Solving problems involving the dot product requires understanding its properties and developing a step-by-step process to solve them. Here are the main steps to follow when solving any general problem involving the dot product:
Identify the problem: Start by reading the problem and...

Dehydration Synthesis

Dehydration Synthesis

Overview
Dehydration synthesis (also called a condensation reaction) is the chemical process in which two molecules covalently link together to form a new molecule, along with the release of a water molecule. Many physiologically important compounds form by dehydration synthesis reactions, such as complex carbohydrates, proteins, DNA, and RNA.
Synthesis of carbohydrates
Sugar molecules are covalently linked together by dehydration synthesis. During the reaction, the hydroxyl (-OH) group from...

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Related Experiment Video

Updated: Feb 4, 2026

Synthesis of Cd-free InP/ZnS Quantum Dots Suitable for Biomedical Applications

Synthesis of Cd-free InP/ZnS Quantum Dots Suitable for Biomedical Applications

Published on: February 6, 2016

Graphene Quantum Dots: Synthesis and Applications.

Ankarao Kalluri¹, Debika Debnath¹, Bhushan Dharmadhikari²

¹Department of Biomedical Engineering, University of Bridgeport, Bridgeport, CT, United States.

Methods in Enzymology

|September 25, 2018

Summary

This summary is machine-generated.

Graphene quantum dots (GQDs), nanoscale graphene derivatives, offer unique properties for biological applications. Their synthesis and characteristics make them promising alternatives to toxic inorganic nanoparticles for cellular studies.

Keywords:

Biomedical Edge effect Graphene Graphene quantum dots Inorganic semiconductors Quantum confinement

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Production and Targeting of Monovalent Quantum Dots

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Last Updated: Feb 4, 2026

Synthesis of Cd-free InP/ZnS Quantum Dots Suitable for Biomedical Applications

Synthesis of Cd-free InP/ZnS Quantum Dots Suitable for Biomedical Applications

Published on: February 6, 2016

Synthesis of In37P20O2CR51 Clusters and Their Conversion to InP Quantum Dots

Synthesis of In37P20O2CR51 Clusters and Their Conversion to InP Quantum Dots

Published on: May 7, 2019

Production and Targeting of Monovalent Quantum Dots

Production and Targeting of Monovalent Quantum Dots

Published on: October 23, 2014

Area of Science:

Materials Science
Nanotechnology
Biomedical Engineering

Background:

Graphene derivatives with nanoscale dimensions exhibit remarkable electronic, optical, chemical, and mechanical properties.
Graphene quantum dots (GQDs) are zero-dimensional graphene derivatives (<20nm) with unique quantum confinement and edge effects.
GQDs possess favorable characteristics including biocompatibility, low toxicity, photostability, and water solubility.

Purpose of the Study:

To provide an overview of graphene quantum dot (GQD) synthesis.
To detail methods for synthesizing GQDs via acidic oxidation of carbon fibers.
To highlight GQDs as suitable nanomaterials for biological system and cellular process research.

Main Methods:

Overview of top-down and bottom-up synthesis approaches for GQDs.
Detailed methodology for GQD synthesis using acidic oxidation of carbon fibers.
Characterization of GQD properties relevant to biological applications.

Main Results:

GQDs exhibit unique properties due to their nanoscale size, quantum confinement, and edge effects.
Acidic oxidation of carbon fibers provides a viable route for GQD synthesis.
GQDs demonstrate excellent biocompatibility, low toxicity, and photostability.

Conclusions:

Graphene quantum dots are versatile nanomaterials with significant potential in biological research.
GQDs can serve as safer, effective replacements for toxic inorganic semiconducting nanoparticles.
The unique properties of GQDs enable detailed molecular-scale understanding of biological systems and cellular processes.